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DTSTART;TZID=America/New_York:20210913T090000
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DTSTAMP:20260502T192358
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UID:10000053-1631523600-1652461200@cmsa.fas.harvard.edu
SUMMARY:Swampland Program
DESCRIPTION:During the 2021–2022 academic year\, the CMSA will host a program on the so-called “Swampland.” \nThe Swampland program aims to determine which low-energy effective field theories are consistent with nonperturbative quantum gravity considerations. Not everything is possible in String Theory\, and finding out what is and what is not strongly constrains the low energy physics. These constraints are naturally interesting for particle physics and cosmology\,  which has led to a great deal of activity in the field in the last years. \nThe Swampland is intrinsically interdisciplinary\, with ramifications in string compactifications\, holography\, black hole physics\, cosmology\, particle physics\, and even mathematics. \nThis program will include an extensive group of visitors and a slate of seminars. Additionally\, the CMSA will host a school oriented toward graduate students. \nMore information will be posted here. \nSeminars\nSwampland Seminar Series & Group Meetings \nProgram Visitors\n\nPieter Bomans\, Princeton\, 10/30/21 – 11/02/21\nIrene Valenzuela\, Instituto de Física Teórica\, 02/14/22 – 02/21/22\nMariana Grana\, CEA/Saclay\, 03/21/22 – 03/25/22\nHector Parra De Freitas\, IPHT Saclay\, 03/21/22 – 04/01/22\nTimo Weigand\, 03/21/22 – 03/28/22\nGary Shiu\, University of Wisconsin-Madison\, 04/03/22 – 04/10/22\nThomas van Riet\, Leuven University\, 04/03/22 – 04/09/22\nLars Aalsma\, University of Wisconsin-Madison\, 04/11/22 – 04/15/22\nSergio Cecotti\, 05/08/22 – 05/21/22\nTom Rudelius\, 05/09/22 – 05/13/22
URL:https://cmsa.fas.harvard.edu/event/swampland-program/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Programs
END:VEVENT
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DTSTART;TZID=America/New_York:20210915T093000
DTEND;TZID=America/New_York:20220525T103000
DTSTAMP:20260502T192358
CREATED:20240213T112446Z
LAST-MODIFIED:20240502T160729Z
UID:10002496-1631698200-1653474600@cmsa.fas.harvard.edu
SUMMARY:CMSA Colloquium 9/15/2021 - 5/25/2022
DESCRIPTION:During the 2021–22 academic year\, the CMSA will be hosting a Colloquium\, organized by Du Pei\, Changji Xu\, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars\, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed. \nSpring 2022\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n1/26/2022\nSamir Mathur (Ohio State University)\nTitle: The black hole information paradox \nAbstract: In 1975\, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997\, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center\,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox\, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown\, using some theorems from quantum information theory\, that these extrapolations were incorrect\, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines\, with a postulate that information would leak out through wormholes. Recently\, it was shown that this wormhole idea had some basic flaws\, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle. \nVideo\n\n\n2/2/2022\nAdam Smith (Boston University)\nTitle: Learning and inference from sensitive data \nAbstract: Consider an agency holding a large database of sensitive personal information—say\,  medical records\, census survey answers\, web searches\, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records. \nI will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically\, why such models must sometimes memorize training data points nearly completely. On the more positive side\, I will present differential privacy\, a rigorous definition of privacy in statistical databases that is now widely studied\, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics\, and lay out directions for future investigation.\n\n\n2/8/2022\nWenbin Yan (Tsinghua University)\n(special time: 9:30 pm ET)\nTitle: Tetrahedron instantons and M-theory indices \nAbstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk\, we will review instanton moduli spaces\, explain the construction\, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory. \nVideo\n\n\n2/16/2022\nTakuro Mochizuki (Kyoto University)\nTitle: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles \nAbstract: In 1960’s\, Narasimhan and Seshadri discovered the equivalence\nbetween irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s\, Donaldson\, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles\nand stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then\, many interesting generalizations have been studied. \nIn this talk\, we would like to review a stream in the study of such correspondences for Higgs bundles\, integrable connections\, $D$-modules and periodic monopoles.\n\n\n2/23/2022\nBartek Czech (Tsinghua University)\nTitle: Holographic Cone of Average Entropies and Universality of Black Holes \nAbstract:  In the AdS/CFT correspondence\, the holographic entropy cone\, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual\, is currently known only up to n=5 regions. I explain that average\nentropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily\, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average\nEntropies” (HCAE). I conjecture the exact form of HCAE\, and find that it has the following properties: (1) HCAE is the simplest it could be\, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture\, the extremal rays of HCAE represent stages of unitary black hole evaporation\, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel\, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n\, namely its bounding inequalities are n-independent. (6) In a precise sense I describe\, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.\n\n\n3/2/2022\nRichard Kenyon (Yale University)\n\n\n\n3/9/2022\nRichard Tsai (UT Austin)\n\n\n\n3/23/2022\nJoel Cohen (University of Maryland)\n\n\n\n3/30/2022\nRob Leigh (UIUC)\n\n\n\n4/6/2022\nJohannes Kleiner (LMU München)\n\n\n\n4/13/2022\nYuri Manin (Max-Planck-Institut für Mathematik)\n\n\n\n4/20/2022\nTBA\n\n\n\n4/27/2022\nTBA\n\n\n\n5/4/2022\nMelody Chan (Brown University)\n\n\n\n5/11/2022\nTBA\n\n\n\n5/18/2022\nTBA\n\n\n\n5/25/2022\nHeeyeon Kim (Rutgers University)\n\n\n\n\n\nFall 2021\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n9/15/2021\nTian Yang\, Texas A&M\nTitle: Hyperbolic Geometry and Quantum Invariants \nAbstract: There are two very different approaches to 3-dimensional topology\, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk\, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.\n\n\n9/29/2021\nDavid Jordan\, University of Edinburgh\nTitle: Langlands duality for 3 manifolds \nAbstract: Langlands duality began as a deep and still mysterious conjecture in number theory\, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds\, and hence the precise form of Langlands duality for them\, remains a mystery. \nIn this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi \, and I will explain a Langlands duality in this setting\, which we have conjectured with Ben-Zvi\, Gunningham and Safronov. \nIntriguingly\, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question\, beyond the scope of the talk.\n\n\n10/06/2021\nPiotr Sulkowski\, U Warsaw\nTitle: Strings\, knots and quivers \nAbstract: I will discuss a recently discovered relation between quivers and knots\, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence\, and it states that various invariants of a given knot are captured by characteristics of a certain quiver\, which can be associated to this knot. Among others\, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver\, it provides a new insight on knot categorification\, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.\n\n\n10/13/2021\nAlexei Oblomkov\, University of Massachusetts\nTitle: Knot homology and sheaves on the Hilbert scheme of points on the plane. \nAbstract: The knot homology (defined by Khovavov\, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However\, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details\, using physics ideas of Kapustin-Rozansky-Saulina\, in the joint work with Rozansky\, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane.  The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane\, the symmetry is the geometric counter-part of the mentioned Poincare duality.\n\n\n10/20/2021\nPeng Shan\, Tsinghua U\nTitle: Categorification and applications \nAbstract: I will give a survey of the program of categorification for quantum groups\, some of its recent development and applications to representation theory.\n\n\n10/27/2021\nKarim Adiprasito\, Hebrew University and University of Copenhagen\nTitle: Anisotropy\, biased pairing theory and applications \nAbstract: Not so long ago\, the relations between algebraic geometry and combinatorics were strictly governed by the former party\, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry\, specifically Hodge Theory. And so\, while we proved analogues for these results\, combinatorics felt subjugated to inspirations from outside of it.\nIn recent years\, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature\, we use intuitions from the Hall marriage theorem\, translated to algebra: once there\, they are statements about self-pairings\, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry\, which in turn established solutions to long-standing conjectures in combinatorics. \nI will survey this theory\, called biased pairing theory\, and new developments within it\, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki\, Vasiliki Petrotou and Johanna Steinmeyer.\n\n\n11/03/2021\nTamas Hausel\, IST Austria\nTitle: Hitchin map as spectrum of equivariant cohomology \nAbstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.\n\n\n11/10/2021\nPeter Keevash\, Oxford\nTitle: Hypergraph decompositions and their applications \nAbstract: Many combinatorial objects can be thought of as a hypergraph decomposition\, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example\, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general\, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs\, which I proved in 2014\, states that\, bar finitely many exceptions\, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting\, which implies an approximate formula for the number of designs; in particular\, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects\, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem)\, whist tournaments or generalised Sudoku squares. In this talk\, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.\n\n\n11/17/2021\nAndrea Brini\, U Sheffield\nTitle: Curve counting on surfaces and topological strings \nAbstract: Enumerative geometry is a venerable subfield of Mathematics\, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s\, in particular\, the interaction with String Theory has sent shockwaves through the subject\, giving both unexpected new perspectives and a remarkably powerful\, physics-motivated toolkit to tackle several traditionally hard questions in the field.\nI will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X\, D)\, with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X\, D)\, including the log Gromov-Witten invariants of the pair\, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety\, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds\, the Donaldson–Thomas theory of a class of symmetric quivers\, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.\n\n\n12/01/2021\nRichard Wentworth\, University of Maryland\nTitle: The Hitchin connection for parabolic G-bundles \nAbstract: For a simple and simply connected complex group G\, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks\, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.\n\n\n12/08/2021\nMaria Chudnovsky\, Princeton\nTitle: Induced subgraphs and tree decompositions \nAbstract: Tree decompositions are a powerful tool in both structural\ngraph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph. \nTree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction\, exploring both the classical notion of bounded tree-width\, and concepts of more structural flavor. This talk will survey some of these ideas and results.\n\n\n12/15/21\nConstantin Teleman (UC Berkeley)\nTitle: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system \nAbstract: I will present a construction of the object in the title which\, applied to the classical Toda system\, controls the theory of categorical representations of compact Lie groups\, along with applications (some conjectural\, some rigorous) to gauged Gromov-Witten theory. Time permitting\, we will review applications to Coulomb branches and the categorified Weyl character formula.
URL:https://cmsa.fas.harvard.edu/event/cmsa-colloquium_2021-22/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220124T090000
DTEND;TZID=America/New_York:20220521T170000
DTSTAMP:20260502T192358
CREATED:20230904T083438Z
LAST-MODIFIED:20240215T103430Z
UID:10000055-1643014800-1653152400@cmsa.fas.harvard.edu
SUMMARY:General Relativity Program
DESCRIPTION:During the Spring 2022 semester\, the CMSA hosted a program on General Relativity. \nThis semester-long program included four minicourses\,  a conference\, and a workshop. \nGeneral Relativity Mincourses: March–May\, 2022 \nGeneral Relativity Conference: April 4–8\, 2022 \nGeneral Relativity Workshop: May 2–5\, 2022 \n  \nProgram Visitors \n\nDan Lee\, CMSA/CUNY\, 1/24/22 – 5/20/22\nStefan Czimek\, Brown\, 2/27/22 – 3/3/22\nLan-Hsuan Huang\, University of Connecticut\, 3/13/22 – 3/19/222\, 3/21/22 – 3/25/22\, 4/17 /22– 4/23/22\nMu-Tao Wang\, Columbia\, 3/21/22 – 3/25/22\, 5/7/22 – 5/9/22\nPo-Ning Chen\, University of California\, Riverside\, 3/21/22 – 3/25/22\,  5/7/22–5/9/22\nMarnie Smith\, Imperial College London\, 3/27/22 – 4/11/22\nChristopher Stith\, University of Michigan\, 3/27/22 – 4/23/22\nMartin Taylor\, Imperial College London\,  3/27/22 – 4/11/22\nMarcelo Disconzi\, Vanderbilt\, 5/9/22 – 5/21/22\nLydia Bieri\, University of Michigan\, 5/5/22 – 5/9/22\n\n 
URL:https://cmsa.fas.harvard.edu/event/general-relativity-program/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Programs
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/GR-Program-Banner_800x450-2.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220301T100000
DTEND;TZID=America/New_York:20220517T130000
DTSTAMP:20260502T192358
CREATED:20240215T103842Z
LAST-MODIFIED:20250328T144509Z
UID:10002743-1646128800-1652792400@cmsa.fas.harvard.edu
SUMMARY:General Relativity Program Minicourses
DESCRIPTION:Minicourses\nGeneral Relativity Program Minicourses \n\nDuring the Spring 2022 semester\, the CMSA hosted a program on General Relativity. \nThis semester-long program included four minicourses running in March\, April\, and May;  a conference April 4–8\, 2022;  and a workshop from May 2–5\, 2022. \n\n  \n\n\n\n\nSchedule\nSpeaker\nTitle\nAbstract\n\n\nMarch 1 – 3\, 2022\n10:00 am – 12:00 pm ET\, each dayLocation: Hybrid. CMSA main seminar room\, G-10.\nDr. Stefan Czimek\nCharacteristic Gluing for the Einstein Equations\nAbstract: This course serves as an introduction to characteristic gluing for the Einstein equations (developed by the lecturer in collaboration with S. Aretakis and I. Rodnianski). First we set up and analyze the characteristic gluing problem along one outgoing null hypersurface.  Then we turn to bifurcate characteristic gluing (i.e.  gluing along two null hypersurfaces bifurcating from a spacelike 2-sphere) and show how to localize characteristic initial data. Subsequently we turn to applications for spacelike initial data. Specifically\, we discuss in detail our alternative proofs of the celebrated Corvino-Schoen gluing to Kerr and the Carlotto-Schoen localization of spacelike initial data (with improved decay).\n\n\nMarch 22 – 25\, 2022\n22nd & 23rd\, 10:00 am – 11:30am ET\n24th & 25th\, 11:00 am – 12:30pm ETLocation: Hybrid. CMSA main seminar room\, G-10.\nProf. Lan-Hsuan Huang\nExistence of Static Metrics with Prescribed Bartnik Boundary Data\nAbstract: The study of static Riemannian metrics arises naturally in general relativity and differential geometry. A static metric produces a special Einstein manifold\, and it interconnects with scalar curvature deformation and gluing. The well-known Uniqueness Theorem of Static Black Holes says that an asymptotically flat\, static metric with black hole boundary must belong to the Schwarzschild family. In the same vein\, most efforts have been made to classify static metrics as known exact solutions. In contrast to the rigidity phenomena and classification efforts\, Robert Bartnik proposed the Static Vacuum Extension Conjecture (originating from his other conjectures about quasi-local masses in the 80’s) that there is always a unique\, asymptotically flat\, static vacuum metric with quite arbitrarily prescribed Bartnik boundary data. In this course\, I will discuss some recent progress confirming this conjecture for large classes of boundary data. The course is based on joint work with Zhongshan An\, and the tentative plan is \n1. The conjecture and an overview of the results\n2. Static regular: a sufficient condition for existence and local uniqueness\n3. Convex boundary\, isometric embedding\, and static regular\n4. Perturbations of any hypersurface are static regular \nVideo on Youtube: March 22\, 2022\n\n\nMarch 29 – April 1\, 2022 10:00am – 12:00pm ET\, each day \nLocation: Hybrid. CMSA main seminar room\, G-10.\nProf. Martin Taylor\nThe nonlinear stability of the Schwarzschild family of black holes\nAbstract: I will present aspects of a theorem\, joint with Mihalis Dafermos\, Gustav Holzegel and Igor Rodnianski\, on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.\n\n\nApril 19 & 21\, 2022\n10 am – 12 pm ET\, each dayZoom only\nProf. Håkan Andréasson\nTwo topics for the Einstein-Vlasov system: Gravitational collapse and properties of static and stationary solutions.\nAbstract: In these lectures I will discuss the Einstein-Vlasov system in the asymptotically flat case. I will focus on two topics; gravitational collapse and properties of static and stationary solutions. In the former case I will present results in the spherically symmetric case that give criteria on initial data which guarantee the formation of black holes in the evolution. I will also discuss the relation between gravitational collapse for the Einstein-Vlasov system and the Einstein-dust system. I will then discuss properties of static and stationary solutions in the spherically symmetric case and the axisymmetric case. In particular I will present a recent result on the existence of massless steady states surrounding a Schwarzschild black hole. \nVideo 4/19/2022 \nVideo 4/22/2022\n\n\nMay 16 – 17\, 2022\n10:00 am – 1:00 pm ET\, each dayLocation: Hybrid. CMSA main seminar room\, G-10.\nProf. Marcelo Disconzi\nA brief overview of recent developments in relativistic fluids\nAbstract: In this series of lectures\, we will discuss some recent developments in the field of relativistic fluids\, considering both the motion of relativistic fluids in a fixed background or coupled to Einstein’s equations. The topics to be discussed will include: the relativistic free-boundary Euler equations with a physical vacuum boundary\, a new formulation of the relativistic Euler equations tailored to applications to shock formation\, and formulations of relativistic fluids with viscosity. \n1. Set-up\, review of standard results\, physical motivation.\n2. The relativistic Euler equations: null structures and the problem of shocks.\n3. The free-boundary relativistic Euler equations with a physical vacuum boundary.\n4. Relativistic viscous fluids. \nVideo 5/16/2022 \nVideo 5/17/2022
URL:https://cmsa.fas.harvard.edu/event/grminicourses/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Workshop
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220418T093000
DTEND;TZID=America/New_York:20220418T110000
DTSTAMP:20260502T192358
CREATED:20230706T180022Z
LAST-MODIFIED:20250328T200252Z
UID:10000094-1650274200-1650279600@cmsa.fas.harvard.edu
SUMMARY:CMSA/Tsinghua Math-Science Literature Lecture: Three Introductory Lectures on Game Theory for Mathematicians: Game Theory Basics and Classical Existence Theorems
DESCRIPTION:Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians \nApril 18\, 2022 | 9:30 – 11:00 am ET \nTitle: Game Theory Basics and Classical Existence Theorems \nAbstract: Games in extensive and normal form. Equilibrium existence theorems by Nash\, von Neumann\, and Zermelo \nTalk chairs: Scott Kominers\, Sergiy Verstyuk \nSLIDES | VIDEO \n 
URL:https://cmsa.fas.harvard.edu/event/maskin_gametheory2022_1/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Mathlit_MASKIN-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220418T130000
DTEND;TZID=America/New_York:20220418T140000
DTSTAMP:20260502T192358
CREATED:20230730T181614Z
LAST-MODIFIED:20240301T072639Z
UID:10001149-1650286800-1650290400@cmsa.fas.harvard.edu
SUMMARY:4/18/2022 Swampland Seminar
DESCRIPTION:Open mic Swampland Discussion \nTopic: Cobordism
URL:https://cmsa.fas.harvard.edu/event/4-18-2022-swampland-seminar/
LOCATION:Virtual
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220419T093000
DTEND;TZID=America/New_York:20220419T103000
DTSTAMP:20260502T192358
CREATED:20230825T080357Z
LAST-MODIFIED:20240304T061057Z
UID:10001295-1650360600-1650364200@cmsa.fas.harvard.edu
SUMMARY:Equivariant Verlinde algebra and quantum K-theory of the moduli space of vortices
DESCRIPTION:Abstract:  In studying complex Chern-Simons theory on a Seifert manifold\, Gukov-Pei proposed an equivariant Verlinde formula\, a one-parameter deformation of the celebrated Verlinde formula. It computes\, among many things\, the graded dimension of the space of holomorphic sections of (powers of) a natural determinant line bundle over the Hitchin moduli space. Gukov-Pei conjectured that the equivariant Verlinde numbers are equal to the equivariant quantum K-invariants of a non-compact (Kahler) quotient space studied by Hanany-Tong. \nIn this talk\, I will explain the setup of this conjecture and its proof via wall-crossing of moduli spaces of (parabolic) Bradlow-Higgs triples. It is based on work in progress with Wei Gu and Du Pei.
URL:https://cmsa.fas.harvard.edu/event/equivariant-verlinde-algebra-and-quantum-k-theory-of-the-moduli-space-of-vortices/
LOCATION:Virtual
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebraic-Geometry-in-String-Theory-04.19.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220419T093000
DTEND;TZID=America/New_York:20220419T103000
DTSTAMP:20260502T192358
CREATED:20240214T070331Z
LAST-MODIFIED:20240304T084706Z
UID:10002554-1650360600-1650364200@cmsa.fas.harvard.edu
SUMMARY:Some combinatorics of Wilson loop diagrams
DESCRIPTION:Abstract: Wilson loop diagrams can be used to study amplitudes in N=4 SYM.  I will set them up and talk about some of their combinatorial aspects\, such as how many Wilson loop diagrams give the same positroid and how to combinatorially read off the dimension and the denominators for the integrands. \n**This talk will be hybrid. Talk will be held at CMSA (20 Garden St) Room G10. \nAll non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival. \nLINK TO FORM
URL:https://cmsa.fas.harvard.edu/event/4-19-2022-combinatorics-physics-and-probability-seminar/
LOCATION:Hybrid
CATEGORIES:Combinatorics Physics and Probability
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Combinatorics-Physics-and-Probability-Seminar-04.19.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220420T093000
DTEND;TZID=America/New_York:20220420T110000
DTSTAMP:20260502T192358
CREATED:20230706T180319Z
LAST-MODIFIED:20250328T200302Z
UID:10000095-1650447000-1650452400@cmsa.fas.harvard.edu
SUMMARY:CMSA/Tsinghua Math-Science Literature Lecture: Three Introductory Lectures on Game Theory for Mathematicians: Mechanism Design
DESCRIPTION:Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians \nApril 20\, 2022 | 9:30 – 11:00 am ET \nTitle: Mechanism Design \nAbstract: Given a social goal\, under what circumstances can we design a game to achieve that goal? \nTalk chairs: Scott Kominers\, Sergiy Verstyuk \nSLIDES | VIDEO
URL:https://cmsa.fas.harvard.edu/event/maskin_gametheory2022_2/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Mathlit_MASKIN-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220420T103000
DTEND;TZID=America/New_York:20220420T130000
DTSTAMP:20260502T192358
CREATED:20240214T101836Z
LAST-MODIFIED:20240229T114304Z
UID:10002664-1650450600-1650459600@cmsa.fas.harvard.edu
SUMMARY:Superconductivity in infinite-layer nickelates
DESCRIPTION:Abstract: Since its discovery\, unconventional superconductivity in cuprates has motivated the search for materials with analogous electronic or atomic structure. We have used soft chemistry approaches to synthesize superconducting infinite layer nickelates from their perovskite precursor phase. We will present the synthesis and transport properties of the nickelates\, observation of a doping-dependent superconducting dome\, and our current understanding of their electronic and magnetic structure.
URL:https://cmsa.fas.harvard.edu/event/4-20-2022-strongly-correlated-quantum-materials-and-high-temperature-superconductors/
CATEGORIES:Strongly Correlated Quantum Materials and High-Temperature Superconductors
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Strongly-Correlated-Quantum-Materials-and-High-Temperature-Superconductors-04.20.21-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220421T090000
DTEND;TZID=America/New_York:20220421T100000
DTSTAMP:20260502T192358
CREATED:20240214T113250Z
LAST-MODIFIED:20240301T103156Z
UID:10002700-1650531600-1650535200@cmsa.fas.harvard.edu
SUMMARY:Secure Multi-Party Computation: from Theory to Practice
DESCRIPTION:Abstract:\nEncryption is the backbone of cybersecurity. While encryption can secure data both in transit and at rest\, in the new era of ubiquitous computing\, modern cryptography also aims to protect data during computation. Secure multi-party computation (MPC) is a powerful technology to tackle this problem\, which enables distrustful parties to jointly perform computation over their private data without revealing their data to each other. Although it is theoretically feasible and provably secure\, the adoption of MPC in real industry is still very much limited as of today\, the biggest obstacle of which boils down to its efficiency. \nMy research goal is to bridge the gap between the theoretical feasibility and practical efficiency of MPC. Towards this goal\, my research spans both theoretical and applied cryptography. In theory\, I develop new techniques for achieving general MPC with the optimal complexity\, bringing theory closer to practice. In practice\, I design tailored MPC to achieve the best concrete efficiency for specific real-world applications. In this talk\, I will discuss the challenges in both directions and how to overcome these challenges using cryptographic approaches. I will also show strong connections between theory and practice. \nBiography:\nPeihan Miao is an assistant professor of computer science at the University of Illinois Chicago (UIC). Before coming to UIC\, she received her Ph.D. from the University of California\, Berkeley in 2019 and had brief stints at Google\, Facebook\, Microsoft Research\, and Visa Research. Her research interests lie broadly in cryptography\, theory\, and security\, with a focus on secure multi-party computation — especially in incorporating her industry experiences into academic research.
URL:https://cmsa.fas.harvard.edu/event/4-21-2022-interdisciplinary-science-seminar/
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-04.21.22-1583x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220421T100000
DTEND;TZID=America/New_York:20220421T110000
DTSTAMP:20260502T192358
CREATED:20240214T095030Z
LAST-MODIFIED:20240301T114330Z
UID:10002648-1650535200-1650538800@cmsa.fas.harvard.edu
SUMMARY:Future stability of the $1+3$ Milne model for the Einstein-Klein-Gordon system
DESCRIPTION:Abstract: We study the small perturbations of the $1+3$-dimensional Milne model for the Einstein-Klein-Gordon (EKG) system. We prove the nonlinear future stability\, and show that the perturbed spacetimes are future causally geodesically complete.  For the proof\, we work within the constant mean curvature (CMC) gauge and focus on the $1+3$ splitting of the Bianchi-Klein-Gordon equations. Moreover\, we treat the Bianchi-Klein-Gordon equations as evolution equations and establish the energy scheme in the sense that we only commute the Bianchi-Klein-Gordon equations with spatially covariant derivatives while normal derivative is not allowed. We propose some refined estimates for lapse and the hierarchies of energy estimates to close the energy argument.
URL:https://cmsa.fas.harvard.edu/event/4-21-2022-general-relativity-seminar/
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220422T093000
DTEND;TZID=America/New_York:20220422T230000
DTSTAMP:20260502T192358
CREATED:20230706T180541Z
LAST-MODIFIED:20250328T200643Z
UID:10000096-1650619800-1650668400@cmsa.fas.harvard.edu
SUMMARY:CMSA/Tsinghua Math-Science Literature Lecture: Three Introductory Lectures on Game Theory for Mathematicians: Auction Theory
DESCRIPTION:Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians \nApril 22\, 2022 | 9:30 – 11:00 am ET \nTitle: Auction Theory \nAbstract: Equivalences among four standard auctions: the high-bid auction (the high bidder wins and pays her bid); the second-bid auction (the high bidder wins and pays the second-highest bid); the Dutch auction (the auctioneer lowers the price successively until some bidder is willing to pay); and the English auction (bidders raise their bids successively until no one wants to bid higher). \nTalk chairs: Scott Kominers\, Sergiy Verstyuk \nSLIDES | VIDEO Answers to Questions from Talks 2 and 3
URL:https://cmsa.fas.harvard.edu/event/maskin_gametheory2022_3/
LOCATION:Virtual
CATEGORIES:Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Mathlit_MASKIN-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220422T153000
DTEND;TZID=America/New_York:20220422T170000
DTSTAMP:20260502T192358
CREATED:20240214T101342Z
LAST-MODIFIED:20240229T112525Z
UID:10002662-1650641400-1650646800@cmsa.fas.harvard.edu
SUMMARY:Higgs = SPT
DESCRIPTION:Speaker: Ruben Verresen \nTitle: Higgs = SPT \nAbstract: The Higgs phase of a gauge theory is important to both fundamental physics (e.g.\, electroweak theory) as well as condensed matter systems (superconductors and other emergent phenomena). However\, such a charge condensate seems subtle and is sometimes described as the spontaneous breaking of gauge symmetry (or a global subgroup). In this talk\, I will argue that the Higgs phase is best understood as a symmetry-protected topological (SPT) phase. The concept of SPT phases arose out of the condensed matter community\, to describe systems with short-range entanglement and edge modes which cannot be removed in the presence of certain symmetries. The perspective that the Higgs phase is an SPT phase recovers known properties of the Higgs phase and provides new insights. In particular\, we revisit the Fradkin-Shenker model and the distinction between the Higgs and confined phases of a gauge theory.
URL:https://cmsa.fas.harvard.edu/event/4-22-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-Seminar-04.22.22-1583x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220426T090000
DTEND;TZID=America/New_York:20220426T100000
DTSTAMP:20260502T192358
CREATED:20240214T071014Z
LAST-MODIFIED:20240304T055455Z
UID:10002555-1650963600-1650967200@cmsa.fas.harvard.edu
SUMMARY:Algebraic Statistics with a View towards Physics
DESCRIPTION:Abstract: We discuss the algebraic geometry of maximum likelihood estimation from the perspective of scattering amplitudes in particle physics. A guiding examples the moduli space of n-pointed rational curves. The scattering potential plays the role of the log-likelihood function\, and its critical points are solutions to rational function equations. Their number is an Euler characteristic. Soft limit degenerations are combined with certified numerical methods for concrete computations. \n**This talk will be hybrid. Talk will be held at CMSA (20 Garden St) Room G10. \nAll non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival. \nLINK TO FORM
URL:https://cmsa.fas.harvard.edu/event/4-26-2022-combinatorics-physics-and-probability-seminar/
CATEGORIES:Combinatorics Physics and Probability
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Combinatorics-Physics-and-Probability-Seminar-04.26.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220426T093000
DTEND;TZID=America/New_York:20220426T103000
DTSTAMP:20260502T192358
CREATED:20230825T080553Z
LAST-MODIFIED:20240304T061555Z
UID:10001296-1650965400-1650969000@cmsa.fas.harvard.edu
SUMMARY:Modularity of mirror families of log Calabi–Yau surfaces
DESCRIPTION:Abstract:   In “Mirror symmetry for log Calabi–Yau surfaces I\,” given a smooth log Calabi–Yau surface pair (Y\,D)\, Gross–Hacking–Keel constructed its mirror family as the spectrum of an explicit algebra whose structure coefficients are determined by the enumerative geometry of (Y\,D). As a follow-up of the work of Gross–Hacking–Keel\, when (Y\,D) is positive\, we prove the modularity of the mirror family as the universal family of log Calabi-Yau surface pairs deformation equivalent to (Y\,D) with at worst du Val singularities. As a corollary\, we show that the ring of regular functions of a smooth affine log Calabi–Yau surface has a canonical basis of theta functions. The key step towards the proof of the main theorem is the application of the tropical construction of singular cycles and explicit formulas of period integrals given in the work of Helge–Siebert. This is joint work with Jonathan Lai.
URL:https://cmsa.fas.harvard.edu/event/modularity-of-mirror-families-of-log-calabi-yau-surfaces/
LOCATION:Virtual
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebraic-Geometry-in-String-Theory-04.26.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220427T090000
DTEND;TZID=America/New_York:20220429T170000
DTSTAMP:20260502T192358
CREATED:20230706T180811Z
LAST-MODIFIED:20250305T172643Z
UID:10000098-1651050000-1651251600@cmsa.fas.harvard.edu
SUMMARY:Workshop on Nonlinear Algebra and Combinatorics from Physics
DESCRIPTION:On April 27–29\, 2022\, the CMSA hosted a workshop on Nonlinear Algebra and Combinatorics. \nOrganizers: Bernd Sturmfels (MPI Leipzig) and Lauren Williams (Harvard). \nIn recent years\, ideas from integrable systems and scattering amplitudes have led to advances in nonlinear algebra and combinatorics. In this short workshop\, aimed at younger participants in the field\, we will explore some of the interactions between the above topics. \nSpeakers: \n\nFederico Ardila (San Francisco State)\nNima Arkani-Hamed (IAS)\nMadeline Brandt (Brown)\nNick Early (Max Planck Institute)\nChris Eur (Harvard)\nClaudia Fevola (Max Planck Institute)\nChristian Gaetz (Harvard)\nYuji Kodama (Ohio State University)\nYelena Mandelshtam (Berkeley)\nSebastian Mizera (IAS)\nMatteo Parisi (Harvard CMSA)\nEmma Previato (Boston University)\nAnna Seigal (Harvard)\nMelissa Sherman-Bennett (University of Michigan)\nSimon Telen (Max Planck Institute)\nCharles Wang (Harvard)\n\n\nSchedule\nWednesday\, April 27\, 2022 \n\n\n\n\n9:30 am–10:30 am\nFederico Ardila\nTitle: Nonlinear spaces from linear spaces \nAbstract: Matroid theory provides a combinatorial model for linearity\, but it plays useful roles beyond linearity. In the classical setup\, a linear subspace V of an n-dimensional vector space gives rise to a matroid M(V) on {1\,…\,n}. However\, the matroid M(V) also knows about some nonlinear geometric spaces related to V. Conversely\, those nonlinear spaces teach us things we didn’t know about matroids. My talk will discuss some examples.\n\n\n10:30 am–11:00 am\nCOFFEE BREAK\n\n\n\n11:00 am–11:45 am\nChris Eur\nTitle: Tautological classes of matroids \nAbstract: Algebraic geometry has furnished fruitful tools for studying matroids\, which are combinatorial abstractions of hyperplane arrangements. We first survey some recent developments\, pointing out how these developments remained partially disjoint. We then introduce certain vector bundles (K-classes) on permutohedral varieties\, which we call “tautological bundles (classes)” of matroids\, as a new framework that unifies\, recovers\, and extends these recent developments. Our framework leads to new questions that further probe the boundary between combinatorics and geometry. Joint work with Andrew Berget\, Hunter Spink\, and Dennis Tseng.\n\n\n11:45 am–2:00 pm\nLUNCH BREAK\n\n\n\n2:00 pm–2:45 pm\nNick Early\nTitle: Biadjoint Scalars and Associahedra from Residues of Generalized Amplitudes \nAbstract: The associahedron is known to encapsulate physical properties such as the notion of tree-level factorization for one of the simplest Quantum Field Theories\, the biadjoint scalar\, which has only cubic interactions.  I will discuss novel instances of the associahedron and the biadjoint scalar in a class of generalized amplitudes\, discovered by Cachazo\, Early\, Guevara and Mizera\, by taking certain limits thereof. This connection leads to a simple proof of a new realization of the associahedron involving a Minkowski sum of certain positroid polytopes in the second hypersimplex.\n\n\n2:45 pm–3:30 pm\nAnna Seigal\nTitle: Invariant theory for maximum likelihood estimation \nAbstract: I will talk about work to uncover connections between invariant theory and maximum likelihood estimation. I will describe how norm minimization over a torus orbit is equivalent to maximum likelihood estimation in log-linear models. We will see the role played by polytopes and discuss connections to scaling algorithms. Based on joint work with Carlos Améndola\, Kathlén Kohn\, and Philipp Reichenbach.\n\n\n3:30 pm–4:00 pm\nCOFFEE BREAK\n\n\n\n4:00 pm–4:45 pm\nMatteo Parisi\nTitle: Amplituhedra\, Scattering Amplitudes\, and Triangulations \nAbstract: In this talk I will discuss about Amplituhedra – generalizations of polytopes inside the Grassmannian – introduced by physicists to encode interactions of elementary particles in certain Quantum Field Theories. In particular\, I will explain how the problem of finding triangulations of Amplituhedra is connected to computing scattering amplitudes of N=4 super Yang-Mills theory.\nTriangulations of polygons are encoded in the associahedron\, studied by Stasheff in the sixties; in the case of polytopes\, triangulations are captured by secondary polytopes\, constructed by Gelfand et al. in the nineties. Whereas a “secondary” geometry describing triangulations of Amplituhedra is still not known\, and we pave the way for such studies. I will discuss how the combinatorics of triangulations interplays with T-duality from String Theory\, in connection with the Momentum Amplituhedron. A generalization of T-duality led us to discover a striking duality between Amplituhedra of “m=2” type and a seemingly unrelated object – the Hypersimplex. The latter is a polytope which appears in many contexts\, from matroid theory to tropical geometry.\nBased on joint works with Lauren Williams\, Melissa Sherman-Bennett\, Tomasz Lukowski.\n\n\n4:45 pm–5:30 pm\nMelissa Sherman-Bennett\nTitle: The hypersimplex and the m=2 amplituhedron \nAbstract: In this talk\, I’ll continue where Matteo left off. I’ll give some more details about the curious correspondence between the m=2 amplituhedron\, a 2k-dimensional subset of Gr(k\, k+2)\, and the hypersimplex\, an (n-1)-dimensional polytope in R^n. The amplituhedron and hypersimplex are both images of the totally nonnegative Grassmannian under some map (the amplituhedron map and the moment map\, respectively)\, but are different dimensions and live in very different ambient spaces. I’ll talk about joint work with Matteo Parisi and Lauren Williams in which we give a bijection between decompositions of the amplituhedron and decompositions of the hypersimplex (originally conjectured by Lukowski–Parisi–Williams). The hypersimplex decompositions are closely related to matroidal subdivisions. Along the way\, we prove a nice description of the m=2 amplituhedron conjectured by Arkani-Hamed–Thomas–Trnka and give a new decomposition of the m=2 amplituhedron into Eulerian-number-many chambers\, inspired by an analogous triangulation of the hypersimplex into Eulerian-number-many simplices.\n\n\n\n\n  \nThursday\, April 28\, 2022 \n\n\n\n\n9:30 am–10:30 am\nClaudia Fevola\nTitle: Nonlinear Algebra meets Feynman integrals \nAbstract: Feynman integrals play a central role in particle physics in the theory of scattering amplitudes. They form a finite-dimensional vector space and the elements of a basis are named “master integrals” in the physics literature. The number of master integrals has been interpreted in different ways: it equals the dimension of a twisted de Rham cohomology group\, the Euler characteristic of a very affine variety\, and the holonomic rank of a D-module. In this talk\, we are interested in a more general family of integrals that contains Feynman integrals as a special case. We explore this setting using tools coming from nonlinear algebra. This is an ongoing project with Daniele Agostini\, Anna-Laura Sattelberger\, and Simon Telen.\n\n\n10:30 am–11:00 am\nCOFFEE BREAK\n\n\n\n11:00 am–11:45 am\nSimon Telen\nTitle: Landau discriminants \nAbstract: The Landau discriminant is a projective variety containing kinematic parameters for which a Feynman integral can have singularities. We present a definition and geometric properties. We discuss how to compute Landau discriminants using symbolic and numerical methods. Our methods can be used\, for instance\, to compute the Landau discriminant of the pentabox diagram\, which is a degree 12 hypersurface in 6-space. This is joint work with Sebastian Mizera.\n\n\n11:45 am–2:00 pm\nLUNCH BREAK\n\n\n\n2:00 pm–2:45 pm\nChristian Gaetz\nTitle: 1-skeleton posets of Bruhat interval polytopes \nAbstract: Bruhat interval polytopes are a well-studied class of generalized permutohedra which arise as moment map images of various toric varieties and totally positive spaces in the flag variety. I will describe work in progress in which I study the 1-skeleta of these polytopes\, viewed as posets interpolating between weak order and Bruhat order. In many cases these posets are lattices and the polytopes\, despite not being simple\, have interesting h-vectors. In a special case\, work of Williams shows that Bruhat interval polytopes are isomorphic to bridge polytopes\, so that chains in the 1-skeleton poset correspond to BCFW-bridge decompositions of plabic graphs.\n\n\n2:45 pm–3:30 pm\nMadeleine Brandt\nTitle: Top Weight Cohomology of $A_g$ \nAbstract: I will discuss a recent project in computing the top weight cohomology of the moduli space $A_g$ of principally polarized abelian varieties of dimension $g$ for small values of $g$. This piece of the cohomology is controlled by the combinatorics of the boundary strata of a compactification of $A_g$. Thus\, it can be computed combinatorially. This is joint work with Juliette Bruce\, Melody Chan\, Margarida Melo\, Gwyneth Moreland\, and Corey Wolfe.\n\n\n3:30 pm–4:00 pm\nCOFFEE BREAK\n\n\n\n4:00 pm–5:00 pm\nEmma Previato\nTitle: Sigma function on curves with non-symmetric semigroup \nAbstract: We start with an overview of the correspondence between spectral curves and commutative rings of differential operators\, integrable hierarchies of non-linear PDEs and Jacobian vector fields. The coefficients of the operators can be written explicitly in terms of the Kleinian sigma function: Weierstrass’ sigma function was generalized to genus greater than one by Klein\, and is a ubiquitous tool in integrability. The most accessible case is the sigma function of telescopic curves. In joint work with J. Komeda and S. Matsutani\, we construct a curve with non-symmetric Weierstrass semigroup (equivalently\, Young tableau)\, consequently non-telescopic\, and its sigma function. We conclude with possible applications to commutative rings of differential operators.\n\n\n6:00 pm\n\nDinner Banquet\, Gran Gusto Trattoria\n\n\n\n\n  \nFriday\, April 29\, 2022 \n\n\n\n\n9:00 am–10:00 am\nYuji Kodama\nTitle: KP solitons and algebraic curves \nAbstract: It is well-known that soliton solutions of the KdV hierarchy are obtained by singular limits of hyper-elliptic curves. However\, there is no general results for soliton solutions of the KP hierarchy\, KP solitons. In this talk\, I will show that some of the KP solitons are related to the singular space curves associated with certain class of numerical semigroups.\n\n\n10:00 am–10:30 am\nCOFFEE BREAK\n\n\n\n10:30 am–11:15 am\nYelena Mandelshtam\nTitle: Curves\, degenerations\, and Hirota varieties \nAbstract: The Kadomtsev-Petviashvili (KP) equation is a differential equation whose study yields interesting connections between integrable systems and algebraic geometry. In this talk I will discuss solutions to the KP equation whose underlying algebraic curves undergo tropical degenerations. In these cases\, Riemann’s theta function becomes a finite exponential sum that is supported on a Delaunay polytope. I will introduce the Hirota variety which parametrizes all KP solutions arising from such a sum. I will then discuss a special case\, studying the Hirota variety of a rational nodal curve. Of particular interest is an irreducible subvariety that is the image of a parameterization map. Proving that this is a component of the Hirota variety entails solving a weak Schottky problem for rational nodal curves. This talk is based on joint work with Daniele Agostini\, Claudia Fevola\, and Bernd Sturmfels.\n\n\n11:15 am–12:00 pm\nCharles Wang\nTitle: Differential Algebra of Commuting Operators \nAbstract: In this talk\, we will give an overview of the problem of finding the centralizer of a fixed differential operator in a ring of differential operators\, along with connections to integrable hierarchies and soliton solutions to e.g. the KdV or KP equations. Given these interesting connections\, it is important to be able to compute centralizers of differential operators\, and we discuss how to use techniques from differential algebra to approach this question\, as well as how having these computational tools can help in understanding the structure of soliton solutions to these equations.\n\n\n12:00 pm–2:00 pm\nLUNCH BREAK\n\n\n\n2:00 pm–3:00 pm\nSebastian Mizera\nTitle: Feynman Polytopes \nAbstract: I will give an introduction to a class of polytopes that recently emerged in the study of scattering amplitudes in quantum field theory.\n\n\n3:00 pm–3:30 pm\nCOFFEE BREAK\n\n\n\n3:30 pm–4:30 pm\nNima Arkani-Hamed\nTitle: Spacetime\, Quantum Mechanics and Combinatorial Geometries at Infinity
URL:https://cmsa.fas.harvard.edu/event/workshop-on-nonlinear-algebra-and-combinatorics-from-physics/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Workshop
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Nonlinear-Workshop_4.27-29.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220427T093000
DTEND;TZID=America/New_York:20220427T103000
DTSTAMP:20260502T192358
CREATED:20240214T034934Z
LAST-MODIFIED:20240304T073208Z
UID:10002515-1651051800-1651055400@cmsa.fas.harvard.edu
SUMMARY:Long common subsequences between bit-strings and the zero-rate threshold of deletion-correcting codes
DESCRIPTION:Speaker: Venkatesan Guruswami\, UC Berkeley \nTitle: Long common subsequences between bit-strings and the zero-rate threshold of deletion-correcting codes \nAbstract: Suppose we transmit n bits on a noisy channel that deletes some fraction of the bits arbitrarily. What’s the supremum p* of deletion fractions that can be corrected with a binary code of non-vanishing rate? Evidently p* is at most 1/2 as the adversary can delete all occurrences of the minority bit. It was unknown whether this simple upper bound could be improved\, or one could in fact correct deletion fractions approaching 1/2.\nWe show that there exist absolute constants A and delta > 0 such that any subset of n-bit strings of size exp((log n)^A) must contain two strings with a common subsequence of length (1/2+delta)n. This immediately implies that the zero-rate threshold p* of worst-case bit deletions is bounded away from 1/2. \nOur techniques include string regularity arguments and a structural lemma that classifies bit-strings by their oscillation patterns. Leveraging these tools\, we find in any large code two strings with similar oscillation patterns\, which is exploited to find a long common subsequence. \nThis is joint work with Xiaoyu He and Ray Li.
URL:https://cmsa.fas.harvard.edu/event/long-common-subsequences-between-bit-strings-and-the-zero-rate-threshold-of-deletion-correcting-codes/
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-04.27.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220428T103000
DTEND;TZID=America/New_York:20220428T120000
DTSTAMP:20260502T192358
CREATED:20240214T101152Z
LAST-MODIFIED:20240229T112257Z
UID:10002661-1651141800-1651147200@cmsa.fas.harvard.edu
SUMMARY:Aspects of 4d supersymmetric dynamics and geometry
DESCRIPTION:Abstract: We will overview the program of geometrically engineering four dimensional supersymmetric QFTs as compactifications of six dimensional SCFTs. In particular we will discuss how strong coupling phenomena in four dimensions\, such as duality and emergence of symmetry\, can be better understood in such geometric constructions.
URL:https://cmsa.fas.harvard.edu/event/4-28-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-Seminar-04.28.22-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220428T130000
DTEND;TZID=America/New_York:20220428T143000
DTSTAMP:20260502T192358
CREATED:20230824T174429Z
LAST-MODIFIED:20240304T081149Z
UID:10001813-1651150800-1651156200@cmsa.fas.harvard.edu
SUMMARY:Building active nematic and active polar liquids out of biological machines
DESCRIPTION:Speaker: Guillaume Duclos (Brandeis)\n\n\nTitle: Building active nematic and active polar liquids out of biological machines\nAbstract: Active matter describes out-of-equilibrium materials composed of motile building blocks that convert free energy into mechanical work. The continuous input of energy at the particle scale liberates these systems from the constraints of thermodynamic equilibrium\, leading to emergent collective behaviors not found in passive materials. In this talk\, I will describe our recent efforts to build simple active systems composed of purified proteins and identify generic emergent behaviors in active systems. I will first discuss two distinct activity-driven instabilities in suspensions of microtubules and molecular motors. Second\, I will describe a new model system for polar fluid whose collective dynamics are driven by the non-equilibrium turnover of actin filaments. Our results illustrate how biomimetic materials can serve as a platform for studying non-equilibrium statistical mechanics\, as well as shine light on the physical mechanisms that regulate self-organization in living matter. \n  \nVideo (Youtube)
URL:https://cmsa.fas.harvard.edu/event/building-active-nematic-and-active-polar-liquids-out-of-biological-machines/
LOCATION:Virtual
CATEGORIES:Active Matter Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Active-Matter-Seminar-04.28.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220428T153300
DTEND;TZID=America/New_York:20220428T173300
DTSTAMP:20260502T192358
CREATED:20240214T112923Z
LAST-MODIFIED:20240301T103000Z
UID:10002698-1651159980-1651167180@cmsa.fas.harvard.edu
SUMMARY:Intersection number and systole on hyperbolic surfaces
DESCRIPTION:Abstract: Let X be a compact hyperbolic surface. We can see that there is a constant C(X) such that the intersection number of the closed geodesics is  \leq C(X) times the product of their lengths. Consider the optimum constant C(X). In this talk\, we describe its asymptotic behavior in terms of systole\,  length of the shortest closed geodesic on X.
URL:https://cmsa.fas.harvard.edu/event/4-28-2022-interdisciplinary-science-seminar/
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-04.28.22-1583x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220428T153500
DTEND;TZID=America/New_York:20220428T163500
DTSTAMP:20260502T192358
CREATED:20240301T114205Z
LAST-MODIFIED:20240301T114205Z
UID:10002896-1651160100-1651163700@cmsa.fas.harvard.edu
SUMMARY:A new proof for the nonlinear stability of slowly-rotating Kerr-de Sitter
DESCRIPTION:Abstract: The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk\, I will present a novel proof of the nonlinear stability of slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space techniques outside of a neighborhood of the trapped set. The proof uses vectorfield techniques to uncover a spectral gap corresponding to exponential decay at the level of the linearized equation. The exponential decay of solutions to the linearized problem is then used in a bootstrap proof to conclude nonlinear stability.
URL:https://cmsa.fas.harvard.edu/event/4-28-2022-general-relativity-seminar/
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220429T093000
DTEND;TZID=America/New_York:20220429T110000
DTSTAMP:20260502T192358
CREATED:20240215T100221Z
LAST-MODIFIED:20240229T090935Z
UID:10002735-1651224600-1651230000@cmsa.fas.harvard.edu
SUMMARY:Machine Learning the Gravity Equation for International Trade
DESCRIPTION:Member Seminar \nSpeaker: Sergiy Verstyuk \nTitle: Machine Learning the Gravity Equation for International Trade \nAbstract: We will go through modern deep learning methods and existing approaches to their interpretation. Next\, I will describe a graph neural network framework. You will also be introduced to an economic analog of gravity. Finally\, we will see how these tools can help understand observed trade flows between 181 countries over 68 years. [Joint work with Michael R. Douglas.]
URL:https://cmsa.fas.harvard.edu/event/4-29-2022-member-seminar/
LOCATION:Virtual
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220502T090000
DTEND;TZID=America/New_York:20220505T170000
DTSTAMP:20260502T192358
CREATED:20230706T181102Z
LAST-MODIFIED:20240109T213327Z
UID:10000100-1651482000-1651770000@cmsa.fas.harvard.edu
SUMMARY:General Relativity Workshop
DESCRIPTION:General Relativity Workshop on scalar curvature\, minimal surfaces\, and initial data sets \nDates: May 2–5\, 2022 \nLocation: Room G10\, CMSA\, 20 Garden Street\, Cambridge MA 02138 and via Zoom webinar.\nAdvanced registration for in-person components is required. \nOrganizers: Dan Lee (CMSA/CUNY)\, Martin Lesourd (CMSA/BHI)\, and Lan-Hsuan Huang (University of Connecticut). \nSpeakers: \n\nZhongshan An\, University of Connecticut\nPaula Burkhardt-Guim\, NYU\nHyun Chul Jang\, University of Miami\nChao Li\, NYU\nChristos Mantoulidis\, Rice University\nRobin Neumayer\, Carnegie Mellon University\nAndre Neves\, University of Chicago\nTristan Ozuch\, MIT\nAnnachiara Piubello\, University of Miami\nAntoine Song\, UC Berkeley\nTin-Yau Tsang\, UC Irvine\nRyan Unger\, Princeton\nZhizhang Xie\, Texas A & M\nXin Zhou\, Cornell University\nJonathan Zhu\, Princeton University\n\nSchedule\nMonday\, May 2\, 2022 \n\n\n\n\n9:30–10:30 am\nHyun Chul Jang\nTitle: Mass rigidity for asymptotically locally hyperbolic manifolds with boundary \nAbstract: Asymptotically locally hyperbolic (ALH) manifolds are a class of manifolds whose sectional curvature converges to −1 at infinity. If a given ALH manifold is asymptotic to a static reference manifold\, the Wang-Chruściel-Herzlich mass integrals are well-defined\, which is a geometric invariant that essentially measure the difference from the reference manifold. In this talk\, I will present the result that an ALH manifold which minimize the mass integrals admits a static potential. To show this\, we proved the scalar curvature map is locally surjective when it is defined on (1) the space of ALH metrics that coincide exponentially toward the boundary or (2) the space of ALH metrics with arbitrarily prescribed nearby Bartnik boundary data. And then\, we establish the rigidity of the known positive mass theorems by studying the static uniqueness. This talk is based on joint work with L.-H. Huang.\n\n\n10:40–11:40 am\nAnnachiara Piubello\nTitle: Estimates on the Bartnik mass and their geometric implications. \nAbstract: In this talk\, we will discuss some recent estimates on the Bartnik mass for data with non-negative Gauss curvature and positive mean curvature. In particular\, if the metric is round the estimate reduces to an estimate found by Miao and if the total mean curvature approaches 0\, the estimate tends to 1/2 the area radius\, which is the bound found by Mantoulidis and Schoen in the blackhole horizon case. We will then discuss some geometric implications. This is joint work with Pengzi Miao.\n\n\nLUNCH BREAK\n\n\n\n\n1:30–2:30 pm\nRyan Unger\nTitle: Density and positive mass theorems for black holes and incomplete manifolds \nAbstract: We generalize the density theorems for the Einstein constraint equations of Corvino-Schoen and Eichmair-Huang-Lee-Schoen to allow for marginally outer trapped boundaries (which correspond physically to apparent horizons). As an application\, we resolve the spacetime positive mass theorem in the presence of MOTS boundary in the non-spin case. This also has a surprising application to the Riemannian setting\, including a non-filling result for manifolds with negative mass. This is joint work with Martin Lesourd and Dan Lee.\n\n\n2:40–3:40 pm\nZhizhang Xie\nTitle: Gromov’s dihedral extremality/rigidity conjectures and their applications I \nAbstract: Gromov’s dihedral extremality and rigidity conjectures concern comparisons of scalar curvature\, mean curvature and dihedral angle for compact manifolds with corners. They have very interesting consequences in geometry and mathematical physics. The conjectures themselves can in some sense be viewed as “localizations” of the positive mass theorem. I will explain some recent work on positive solutions to these conjectures and some related applications (such as a positive solution to the Stoker conjecture). The talks are based on my joint works with Jinmin Wang and Guoliang Yu.\n\n\nTEA BREAK\n\n\n\n\n4:10–5:10 pm\nAntoine Song (virtual)\nTitle: The spherical Plateau problem \nAbstract: For any closed oriented manifold with fundamental group G\, or more generally any group homology class for a group G\, I will discuss an infinite codimension Plateau problem in a Hilbert classifying space for G. For instance\, for a closed oriented 3-manifold M\, the intrinsic geometry of any Plateau solution is given by the hyperbolic part of M.\n\n\n\n\nTuesday\, May 3\, 2022 \n\n\n\n\n9:30–10:30 am\nChao Li\nTitle: Stable minimal hypersurfaces in 4-manifolds \nAbstract: There have been a classical theory for complete minimal surfaces in 3-manifolds\, including the stable Bernstein conjecture in R^3 and rigidity results in 3-manifolds with positive Ricci curvature. In this talk\, I will discuss how one may extend these results in four dimensions. This leads to new comparison theorems for positively curved 4-manifolds.\n\n\n10:40–11:40 am\nRobin Neumayer\nTitle: An Introduction to $d_p$ Convergence of Riemannian Manifolds I \nAbstract: What can you say about the structure or a-priori regularity of a Riemannian manifold if you know certain bounds on its curvature? To understand this question\, it is often important to understand in what sense a sequence of Riemannian manifolds (possessing a given curvature constraint) will converge\, and what the limiting objects look like. In this mini-course\, we introduce the notions of $d_p$ convergence of Riemannian manifolds and of rectifiable Riemannian spaces\, the objects that arise as $d_p$ limits. This type of convergence can be useful in contexts when the distance functions of the Riemannian manifolds are not uniformly controlled. This course is based on joint work with Man Chun Lee and Aaron Naber.\n\n\nLUNCH BREAK\n\n\n\n\n1:30–2:30 pm\nZhongshan An\nTitle: Local existence and uniqueness of static vacuum extensions of Bartnik boundary data \nAbstract: The study of static vacuum Riemannian metrics arises naturally in differential geometry and general relativity. It plays an important role in scalar curvature deformation\, as well as in constructing Einstein spacetimes. Existence of static vacuum Riemannian metrics with prescribed Bartnik data — the induced metric and mean curvature of the boundary — is one of the most fundamental problems in Riemannian geometry related to general relativity. It is also a very interesting problem on the global solvability of a natural geometric boundary value problem. In this talk I will first discuss some basic properties of the nonlinear and linearized static vacuum equations and the geometric boundary conditions. Then I will present some recent progress towards the existence problem of static vacuum metrics based on joint works with Lan-Hsuan Huang.\n\n\n2:40–3:40 pm\nZhizhang Xie\nTitle: Gromov’s dihedral extremality/rigidity conjectures and their applications II \nAbstract: Gromov’s dihedral extremality and rigidity conjectures concern comparisons of scalar curvature\, mean curvature and dihedral angle for compact manifolds with corners. They have very interesting consequences in geometry and mathematical physics. The conjectures themselves can in some sense be viewed as “localizations” of the positive mass theorem. I will explain some recent work on positive solutions to these conjectures and some related applications (such as a positive solution to the Stoker conjecture). The talks are based on my joint works with Jinmin Wang and Guoliang Yu.\n\n\nTEA BREAK\n\n\n\n\n4:10–5:10 pm\nTin-Yau Tsang\nTitle: Dihedral rigidity\, fill-in and spacetime positive mass theorem \nAbstract: For compact manifolds with boundary\, to characterise the relation between scalar curvature and boundary geometry\, Gromov proposed dihedral rigidity conjecture and fill-in conjecture. In this talk\, we will see the role of spacetime positive mass theorem in answering the corresponding questions for initial data sets.\n\n\n\n\nSpeakers Banquet\n\n\n\n\nWednesday\, May 4\, 2022 \n\n\n\n\n9:30–10:30 am\nTristan Ozuch\nTitle: Weighted versions of scalar curvature\, mass and spin geometry for Ricci flows \nAbstract: With A. Deruelle\, we define a Perelman-like functional for ALE metrics which lets us study the (in)stability of Ricci-flat ALE metrics. With J. Baldauf\, we extend some classical objects and formulas from the study of scalar curvature\, spin geometry and general relativity to manifolds with densities. We surprisingly find that the extension of ADM mass is the opposite of the above functional introduced with A. Deruelle. Through a weighted Witten’s formula\, this functional also equals a weighted spinorial Dirichlet energy on spin manifolds. Ricci flow is the gradient flow of all of these quantities.\n\n\n10:40–11:40 am\nRobin Neumayer\nTitle: An Introduction to $d_p$ Convergence of Riemannian Manifolds II \nAbstract: What can you say about the structure or a-priori regularity of a Riemannian manifold if you know certain bounds on its curvature? To understand this question\, it is often important to understand in what sense a sequence of Riemannian manifolds (possessing a given curvature constraint) will converge\, and what the limiting objects look like. In this mini-course\, we introduce the notions of $d_p$ convergence of Riemannian manifolds and of rectifiable Riemannian spaces\, the objects that arise as $d_p$ limits. This type of convergence can be useful in contexts when the distance functions of the Riemannian manifolds are not uniformly controlled. This course is based on joint work with Man Chun Lee and Aaron Naber.\n\n\nLUNCH BREAK\n\n\n\n\n1:30–2:30 pm\nChristos Mantoulidis\nTitle: Metrics with lambda_1(-Delta+kR) > 0 and applications to the Riemannian Penrose Inequality \nAbstract: On a closed n-dimensional manifold\, consider the space of all Riemannian metrics for which -Delta+kR is positive (nonnegative) definite\, where k > 0 and R is the scalar curvature. This spectral generalization of positive (nonnegative) scalar curvature arises naturally\, for different values of k\, in the study of scalar curvature in dimension n + 1 via minimal surfaces\, the Yamabe problem in dimension n\, and Perelman’s surgery for Ricci flow in dimension n = 3. We study these spaces in unison and generalize\, as appropriate\, scalar curvature results that we eventually apply to k = 1/2\, where the space above models apparent horizons in time-symmetric initial data sets to the Einstein equations and whose flexibility properties are intimately tied with the instability of the Riemannian Penrose Inequality. This is joint work with Chao Li.\n\n\n2:40–3:40 pm\nZhizhang Xie\nTitle: Gromov’s dihedral extremality/rigidity conjectures and their applications III \nAbstract: Gromov’s dihedral extremality and rigidity conjectures concern comparisons of scalar curvature\, mean curvature and dihedral angle for compact manifolds with corners. They have very interesting consequences in geometry and mathematical physics. The conjectures themselves can in some sense be viewed as “localizations” of the positive mass theorem. I will explain some recent work on positive solutions to these conjectures and some related applications (such as a positive solution to the Stoker conjecture). The talks are based on my joint works with Jinmin Wang and Guoliang Yu.\n\n\nTEA BREAK\n\n\n\n\n4:10–5:10 pm\nXin Zhou\n(Virtual)\nTitle: Min-max minimal hypersurfaces with higher multiplicity \nAbstract: It is well known that minimal hypersurfaces produced by the Almgren-Pitts min-max theory are counted with integer multiplicities. For bumpy metrics (which form a generic set)\, the multiplicities are one thanks to the resolution of the Marques-Neves Multiplicity One Conjecture. In this talk\, we will exhibit a set of non-bumpy metrics on the standard (n+1)-sphere\, in which the min-max varifold associated with the second volume spectrum is a multiplicity two n-sphere. Such non-bumpy metrics form the first set of examples where the min-max theory must produce higher multiplicity minimal hypersurfaces. The talk is based on a joint work with Zhichao Wang (UBC).\n\n\n\n\nMay 5\, 2022 \n\n\n\n\n9:00–10:00 am\nAndre Neves\nTitle: Metrics on spheres where all the equators are minimal \nAbstract: I will talk about joint work with Lucas Ambrozio and Fernando Marques where we study the space of metrics where all the equators are minimal.\n\n\n10:10–11:10 am\nRobin Neumayer\nTitle: An Introduction to $d_p$ Convergence of Riemannian Manifolds III \nAbstract: What can you say about the structure or a-priori regularity of a Riemannian manifold if you know certain bounds on its curvature? To understand this question\, it is often important to understand in what sense a sequence of Riemannian manifolds (possessing a given curvature constraint) will converge\, and what the limiting objects look like. In this mini-course\, we introduce the notions of $d_p$ convergence of Riemannian manifolds and of rectifiable Riemannian spaces\, the objects that arise as $d_p$ limits. This type of convergence can be useful in contexts when the distance functions of the Riemannian manifolds are not uniformly controlled. This course is based on joint work with Man Chun Lee and Aaron Naber.\n\n\n11:20–12:20 pm\nPaula Burkhardt-Guim\nTitle: Lower scalar curvature bounds for C^0 metrics: a Ricci flow approach \nAbstract: We describe some recent work that has been done to generalize the notion of lower scalar curvature bounds to C^0 metrics\, including a localized Ricci flow approach. In particular\, we show the following: that there is a Ricci flow definition which is stable under greater-than-second-order perturbation of the metric\, that there exists a reasonable notion of a Ricci flow starting from C^0 initial data which is smooth for positive times\, and that the weak lower scalar curvature bounds are preserved under evolution by the Ricci flow from C^0 initial data.\n\n\nLUNCH BREAK\n\n\n\n\n1:30–2:30 pm\nJonathan Zhu\nTitle: Widths\, minimal submanifolds and symplectic embeddings \nAbstract: Width or waist inequalities measure the size of a manifold with respect to measures of families of submanifolds. We’ll discuss related area estimates for minimal submanifolds\, as well as applications to quantitative symplectic camels.
URL:https://cmsa.fas.harvard.edu/event/grworkshop/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Workshop
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/GR-Workshop-Poster.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220503T093000
DTEND;TZID=America/New_York:20220503T103000
DTSTAMP:20260502T192358
CREATED:20240214T072025Z
LAST-MODIFIED:20240304T055241Z
UID:10002557-1651570200-1651573800@cmsa.fas.harvard.edu
SUMMARY:The threshold for stacked triangulations
DESCRIPTION:Abstract: Consider a bootstrap percolation process that starts with a set of `infected’ triangles $Y \subseteq \binom{[n]}3$\, and a new triangle f gets infected if there is a copy of K_4^3 (= the boundary of a tetrahedron) in which f is the only not-yet infected triangle.\nSuppose that every triangle is initially infected independently with probability p=p(n)\, what is the threshold probability for percolation — the event that all triangles get infected? How many new triangles do get infected in the subcritical regime? \nThis notion of percolation can be viewed as a simplification of simple-connectivity. Namely\, a stacked triangulation of a triangle is obtained by repeatedly subdividing an inner face into three faces.\nWe ask: for which $p$ does the random simplicial complex Y_2(n\,p) contain\, for every triple $xyz$\, the faces of a stacked triangulation of $xyz$ whose internal vertices are arbitrarily labeled in [n]. \nWe consider this problem in every dimension d>=2\, and our main result identifies a sharp probability threshold for percolation\, showing it is asymptotically (c_d*n)^(-1/d)\, where c_d is the growth rate of the Fuss–Catalan numbers of order d. \nThe proof hinges on a second moment argument in the supercritical regime\, and on Kalai’s algebraic shifting in the subcritical regime. \nJoint work with Eyal Lubetzky.
URL:https://cmsa.fas.harvard.edu/event/5-3-2022-cmsa-combinatorics-physics-and-probability-seminar/
LOCATION:Hybrid
CATEGORIES:Combinatorics Physics and Probability
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Combinatorics-Physics-and-Probability-Seminar-05.03.22-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220505T153600
DTEND;TZID=America/New_York:20220505T173600
DTSTAMP:20260502T192358
CREATED:20240214T084023Z
LAST-MODIFIED:20240301T102954Z
UID:10002592-1651764960-1651772160@cmsa.fas.harvard.edu
SUMMARY:Qianfang: a type-safe and data-driven healthcare system starting from Traditional Chinese Medicine
DESCRIPTION:Abstract: Although everyone talks about AI + healthcare\, many people were unaware of the fact that there are two possible outcomes of the collaboration\, due to the inherent dissimilarity between the two giant subjects. The first possibility is healthcare-leads\, and AI is for building new tools to make steps in healthcare easier\, better\, more effective or more accurate. The other possibility is AI-leads\, and therefore the protocols of healthcare can be redesigned or redefined to make sure that the whole infrastructure and pipelines are ideal for running AI algorithms. \nOur system Qianfang belongs to the second category. We have designed a new kind of clinic for the doctors and patients\, so that it will be able to collect high quality data for AI algorithms. Interestingly\, the clinic is based on Traditional Chinese Medicine (TCM) instead of modern medicine\, because we believe that TCM is more suitable for AI algorithms as the starting point. \nIn this talk\, I will elaborate on how we convert TCM knowledge into a modern type-safe large-scale system\, the mini-language that we have designed for the doctors and patients\, the interpretability of AI decisions\, and our feedback loop for collecting data. \nOur project is still on-going\, not finished yet.Bio: Yang Yuan is now an assistant professor at IIIS\, Tsinghua. He finished his undergraduate study at Peking University in 2012. Afterwards\, he received his PhD at Cornell University in 2018\, advised by Professor Robert Kleinberg. During his PhD\, he was a visiting student at MIT/Microsoft New England (2014-2015) and Princeton University (2016 Fall). Before joining Tsinghua\, he spent one year at MIT Institute for Foundations of Data Science (MIFODS) as a postdoc researcher. He now works on AI+Healthcare\, AI Interpretability and AI system.
URL:https://cmsa.fas.harvard.edu/event/5-5-2022-interdisciplinary-science-seminar/
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-05.05.2022-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220506T100000
DTEND;TZID=America/New_York:20220508T170000
DTSTAMP:20260502T192358
CREATED:20230706T181343Z
LAST-MODIFIED:20231227T080733Z
UID:10000104-1651831200-1652029200@cmsa.fas.harvard.edu
SUMMARY:2022 NSF FRG Workshop on Discrete Shapes
DESCRIPTION:On May 6–8\, 2022\, the CMSA  hosted a second NSF FRG Workshop. \nThis project brings together a community of researchers who develop theoretical and computational models to characterize shapes. Their combined interests span Mathematics (Geometry and Topology)\, Computer Science (Scientific Computing and Complexity Theory)\, and domain sciences\, from Data Sciences to Computational Biology. \nScientific research benefits from the development of an ever-growing number of sensors that are able to capture details of the world at increasingly fine resolutions. The seemingly unlimited breadth and depth of these sources provide the means to study complex systems in a more comprehensive way. At the same time\, however\, these sensors are generating a huge amount of data that comes with a high level of complexity and heterogeneity\, providing indirect measurements of hidden processes that provide keys to the systems under study. This has led to new challenges and opportunities in data analysis. Our focus is on image data and the shapes they represent. Advances in geometry and topology have led to powerful new tools that can be applied to geometric methods for representing\, searching\, simulating\, analyzing\, and comparing shapes. These methods and tools can be applied in a wide range of fields\, including computer vision\, biological imaging\, brain mapping\, target recognition\, and satellite image analysis. \nThis workshop is part of the NSF FRG project: Geometric and Topological Methods for Analyzing Shapes. \nThe workshop was held in room G10 of the CMSA\, located at 20 Garden Street\, Cambridge\, MA. \n\nWorkshop on Discrete Shapes\nMay 6–8\, 2022\nOrganizers: \n\nDavid Glickenstein (University of Arizona)\nJoel Hass (University of California\, Davis)\nPatrice Koehl (University of California\, Davis)\nFeng Luo (Rutgers University\, New Brunswick)\nMaria Trnkova (University of California\, Davis)\nShing-Tung Yau (Harvard)\n\nSpeakers: \n\nMiri Ben-Chen (Technion)\nAlexander Bobenko (TU Berlin)\nJohn Bowers (James Madison)\nSteven Gortler (Harvard)\nDavid Gu (Stony Brook)\nAnil Hirani (UIUC)\nYanwen Luo (Rutgers)\nPeter Schroeder (Caltech)\nJustin Solomon (MIT)\nTianqi Wu (Clark University)\n\nContributed Talk Speakers: \n\nOded Stein (MIT)\nBohan Zhou (Dartmouth)\n\nSchedule\nSchedule (PDF) \nFriday\, May 6\, 2022 \n\n\n\n\n10:00–10:05 am\n\nWelcome Opening\n\n\n10:05–10:55 am\nAnil N. Hirani\nTitle: Discrete vector bundles with connection \nAbstract: We have recently initiated a generalization of discrete exterior calculus to differential forms with values in a vector bundle. A discrete vector bundle with connection over a simplicial complex has fibers at vertices and transport maps on edges\, just as in lattice gauge theory. The first part of this work involves defining and examining properties of a combinatorial exterior covariant derivative and wedge product. We find that these operators commute with pullback under simplicial maps of the base space. From these definitions emerges a combinatorial curvature. In the second part of this work we showed that the curvature behaves as one expects: it measures failure of parallel transport to be independent of the path\, and is the local obstruction to a trivialization. For a bundle with metric\, metric compatibility of the discrete connection is equivalent to a Leibniz rule.  Vanishing curvature is indeed equivalent to an appropriately defined discrete flat connection\, and curvature obstructs trivializability. In this talk I will focus on just the first part\, and talk about naturality of the discrete exterior covariant derivative and discrete wedge product using simple examples. Joint work with Daniel Berwick-Evans (UIUC) and Mark Schubel (Apple\, Inc.).\n\n\n11:10–12:00 pm\nDavid Gu\nTitle: Surface Quadrilateral Meshing Based on Abel-Jacobi Theory \nAbstract: Surface quadrilateral meshing plays an important role in many fields. For example\, in CAD (computer-aided design)\, all shapes are represented as Spline surfaces\, which requires structured quad-meshing; in CAE (computer-aided engineering)\, the surface tessellation greatly affects the accuracy and efficiency of numerical simulations. Although the research on mesh generation has a long history\, it remains a great challenge to automatically generate structured quad-meshes with high qualities. The key is to find the governing equation for the singularities of the global structured quad-meshes. \nIn this talk\, we introduce our recent discovery:  the singularities of a quad-mesh are governed by the Abel theorem. We show that each quad-mesh determines a conformal structure and a meromorphic quadratic differential\, the configuration of the mesh singularities can be described as the divisor of the differential. The quad-mesh divisor minus four times of the divisor of a holomorphic one-form is principal and satisfies the Abel theorem: its image under the Jacobi map is zero in the Jacobi variety. \nThis leads to a rigorous and efficient algorithm for surface structured quadrilateral meshing. After determining the singularities\, the metric induced by the quad-mesh can be computed using the discrete Yambe flow\, and the meromorphic quartic differential can be constructed\, the trajectories of the differentials give the quad-mesh. The method can be applied directly for geometric modeling and computational mechanics.\n\n\n12:00–2:00 pm\nLunch Break\n\n\n\n2:00–2:50 pm\n Justin Solomon\nTitle:  Geometry Processing with Volumes \nAbstract:  Many algorithms in geometry processing are restricted to two-dimensional surfaces represented as triangle meshes.  Drawing inspiration from simulation\, medical imaging\, and other application domains\, however\, there is a substantial demand for geometry processing algorithms targeted to volumes represented as tetrahedral meshes or grids.  In this talk\, I will summarize some efforts in our group to develop a geometry processing toolkit specifically for volumes.  Specifically\, I will cover our recent work on hexahedral remeshing via cuboid decomposition\, volumetric correspondence\, and minimal surface computation via geometric measure theory.\n\n\n3:00–3:20 pm\nOded Stein\nTitle: Optimization for flip-free parametrization \nAbstract: Parametrizations without flipped elements are desirable in a variety of applications such as UV mapping and surface/volume correspondence. Computing flip-free parametrizations can be challenging\, and there are many different approaches to the problem. In this talk we will look at multiple strategies for flip-free parametrizations that are based on the optimization of continuous energies. Due to the nature of the problem\, these energies are often nonconvex and unbounded\, which is a challenge for optimization methods. We will also take a closer look at our recently developed method for computing flip-free parametrizations using the Alternating Direction Method of Multipliers (ADMM).\n\n\n3:20–4:00 pm\nBreak\n\n\n\n4:00–4:50 pm\nJohn Bowers\nTitle: Koebe-Andre’ev-Thurston Packings via Flow \nAbstract: Recently\, Connelly and Gortler gave a novel proof of the circle packing theorem for tangency packings by introducing a hybrid combinatorial-geometric operation\, flip-and-flow\, that allows two tangency packings whose contact graphs differ by a combinatorial edge flip to be continuously deformed from one to the other while maintaining tangencies across all of their common edges. Starting from a canonical tangency circle packing with the desired number of circles a finite sequence of flip-and-flow operations may be applied to obtain a circle packing for any desired (proper) contact graph with the same number of circles. \nThe full Koebe-Andre’ev-Thurston theorem generalizes the circle packing theorem to allow for neighboring circles to overlap by angles up to $\pi/2$. In this talk I will show that the Connelly-Gortler method can be extended to allow for circles to overlap to angles up to $\pi/2$. This results in a new proof of the general Koebe-Andre’ev-Thurston theorem for disk patterns on $\mathbb{S}^2$ as well as a numerical algorithm for computing them. The proof involves generalizing a notion of convexity for circle polyhedra that was recently used to prove the global rigidity of certain circle packings\, which is then used to show that all convex circle polyhedra are infinitesimally rigid\, a result of independent interest.\n\n\n5:00–5:30 pm\nMovies\n “conform!” & ”Koebe polyhedra”\n\n\n\n\n  \nSaturday\, May 7\, 2022 \n\n\n\n\n9:30–10:20 am\nAlexander Bobenko\nTitle: The Bonnet problem: Is a surface characterized by its metric and curvatures? \nAbstract: We consider a classical problem in differential geometry\, known as the Bonnet problem\, whether a surface is characterized by a metric and mean curvature function. Generically\, the answer is yes. Special cases when it is not the case are classified. In particular\, we explicitly construct a pair of immersed tori that are related by a mean curvature preserving isometry. This resolves a longstanding open problem on whether the metric and mean curvature function determine a unique compact surface. Discrete differential geometry is used to find crucial geometric properties of surfaces. This is a joint work with Tim Hoffmann and Andrew Sageman-Furnas\n\n\n10:20–11:00 am\nBreak\n\n\n\n11:00–11:50 am\nMiri Ben Chen\nTitle: Surface Multigrid via Intrinsic Prolongation \nAbstract: The solution of a linear system is a required ingredient in many geometry processing applications\, and multigrid methods are among the most efficient solution techniques. However\, due to the unstructured nature of triangle meshes\, mapping functions between different multigrid levels is challenging. In this talk I will present our recent work that uses an intrinsic prolongation operator as the main building block in a multigrid solver for curved triangle meshes. Our solver can be used as a black-box in any triangle-mesh based system that requires a linear solve\, and leads to order of magnitude time-efficiency improvement compared to direct solvers.\n\n\n12:00–2:00 pm\nLunch Break\n\n\n\n2:00–2:50 pm\nSteven Gortler\nTitle: Reconstructing configurations and graphs from unlabeled distance measurements \nAbstract: Place a configuration of n  points (vertices) generically in R^d. Measure the Euclidean lengths of m point-pairs (edges). When is the underlying graph determined by these $m$ numbers (up to isomorphism)? When is the point configuration determined by these $m$ numbers (up to congruence)? This question is motivated by a number of inverse problem applications. In this talk\, I will review what is known about this question.\n\n\n3:00–3:20 pm\nBohan Zhou\nTitle: Efficient and Exact Multimarginal Optimal Transport with Pairwise Costs \nAbstract: Optimal transport has profound and wide applications since its introduction in 1781 by Monge. Thanks to the Benamou-Brenier formulation\, it provides a meaningful functional in the image science like image and shape registrations. However\, exact computation through LP or PDE is in general not practical in large scale\, while the popular entropy-regularized method introduces additional diffusion noise\, deteriorating shapes and boundaries. Until the recent work [Jacobs and Leger\, A Fast Approach to Optimal Transport: the back-and-forth method\, Numerische Mathematik\, 2020]\, solving OT in a both accurate and fast fashion finally becomes possible. Multiple marginal optimal transport is a natural extension from OT but has its own interest and is in general more computationally expensive. The entropy method suffers from both diffusion noise and high dimensional computational issues. In this work with Matthew Parno\, we extend from two marginals to multiple marginals\, on a wide class of cost functions when those marginals have a graph structure. This new method is fast and does not introduce diffusion. As a result\, the new proposed method can be used in many fields those require sharp boundaries. If time allows\, we will illustrate by examples the faithful joint recover via MMOT of images with sharp boundaries\, with applications on sea ice prediction.\n\n\n3:20–4:00 pm\nBreak\n\n\n\n4:00–4:50 pm\nPeter Schroeder\nTitle: Constrained Willmore Surfaces \nAbstract: The Willmore energy of a surface is a canonical example of a squared curvature bending energy. Its minimizers are therefore of interest both in the theory of surfaces and in practical applications from physical and geometric modeling. Minimizing the bending energy alone however is insufficient. Taking a cue from univariate splines which incorporate an isometry constraint we consider Willmore minimizers subject to a conformality constraint. In this talk I will report on a numerical algorithm to find such constrained minimizers for triangle meshes. \nJoint work with Yousuf Soliman (Caltech)\, Olga Diamanti (UGraz)\, Albert Chern (UCSD)\, Felix Knöppel (TU Berlin)\, Ulrich Pinkall (TU Berlin).\n\n\n5:00–5:50 pm\n\nProblems and Application discussions\n\n\n\n\n  \nSunday\, May 8\, 2022 \n\n\n\n\n9:00–9:50 am\nTianqi Wu\nTitle: Convergence of discrete uniformizations \nAbstract: The theory of discrete conformality\, based on the notion of vertex scaling\, has been implemented in computing conformal maps or uniformizations of surfaces. We will show that if a Delaunay triangle mesh approximates a smooth surface\, then the related discrete uniformization will converge to the smooth uniformization\, with an error bounded linearly by the size of the triangles in the mesh.\n\n\n10:10–11:00 am\nYanwen Luo\nTitle:  Recent Progress in Spaces of Geodesic Triangulations of Surfaces\n\nAbstract: Spaces of geodesic triangulations of surfaces are natural discretization of the groups of surface diffeomorphisms isotopy to the identity. It has been conjectured that these spaces have the same homotopy type as their smooth counterparts. In this talk\, we will report the recent progress in this problem. The key ingredient is the idea in Tutte’s embedding theorem. We will explain how to use it to identify the homotopy types of spaces of geodesic triangulations. This is joint work with Tianqi Wu and Xiaoping Zhu.\n\n\n11:10–12:00 pm\n\nProblems and Application discussions\n\n\n12:00–1:00 pm\nMovie\n“The Discrete Charm of Geometry”
URL:https://cmsa.fas.harvard.edu/event/2022-nsf-frg-workshop/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Workshop
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/FRG-Poster-1-791x1024-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220509T090000
DTEND;TZID=America/New_York:20220512T123000
DTSTAMP:20260502T192358
CREATED:20230706T181710Z
LAST-MODIFIED:20231227T082643Z
UID:10000107-1652086800-1652358600@cmsa.fas.harvard.edu
SUMMARY:Conference in Memory of Professor Masatake Kuranishi
DESCRIPTION:On May 9–12\, 2022\, the CMSA hosted the conference Deformations of structures and moduli in geometry and analysis: A Memorial in honor of Professor Masatake Kuranishi. \nOrganizers:  Tristan Collins (MIT) and Shing-Tung Yau (Harvard and Tsinghua) \nVideos are available on the conference playlist. \n  \nSpeakers: \nCharles Fefferman (Princeton University) \nTeng Fei (Rutgers University) \nRobert Friedman (Columbia University) \nKenji Fukaya (Simons Center\, Stony Brook) \nAkito Futaki (Tsinghua University) \nVictor Guillemin (Massachusetts Institute of Technology) \nNigel Hitchin (Oxford University) \nBlaine Lawson (Stony Brook University) \nYu-Shen Lin (Boston University) \nMelissa C.C. Liu (Columbia University) \nTakeo Ohsawa (Nagoya University) \nDuong H. Phong (Columbia University) \nSebastien Picard (University of British Columbia) \nPaul Seidel (Massachusetts Institute of Technology) \nGabor Szekelyhidi (University of Notre Dame) \nClaire Voisin (Institut de Mathematiques\, Jussieu\, France) \nShing-Tung Yau (Harvard University) \n  \n\n\n\nSchedule (download pdf) \n\nMonday\, May 9\, 2022 \n\n\n\n8:15 am\nLight breakfast & coffee/tea\n\n\n8:45–9:00 am\nOpening Remarks\n\n\n9:00–10:00 am\nKenji Fukaya\nTitle: Gromov Hausdorff convergence of filtered A infinity category \nAbstract: In mirror symmetry a mirror to a symplectic manifold is actually believed to be a family of complex manifold parametrized by a disk (of radius 0). The coordinate ring of the parameter space is a kind of formal power series ring the Novikov ring. Novikov ring is a coefficient ring of Floer homology. Most of the works on homological Mirror symmetry so far studies A infinity category over Novikov field\, which corresponds to the study of generic fiber. The study of A infinity category over Novikov ring is related to several interesting phenomenon of Hamiltonian dynamics. In this talk I will explain a notion which I believe is useful to study mirror symmetry. \nVideo\n\n\n10:15–11:15 am\nNigel Hitchin (Zoom)\nTitle: Deformations: A personal perspective \nAbstract: The talk\, largely historical\, will focus on different deformation complexes I have encountered in my work\, starting with instantons on 4-manifolds\, but also monopoles\, Higgs bundles and generalized complex structures. I will also discuss some speculative ideas related to surfaces of negative curvature. \nVideo\n\n\n11:30–12:30 pm\nH. Blaine Lawson\nTitle: Projective Hulls\, Projective Linking\, and Boundaries of Varieties \nAbstract: In 1958 John Wermer proved that the polynomial hull of a compact real analytic curve γ ⊂ Cn was a 1-dim’l complex subvariety of Cn − γ. This result engendered much subsequent activity\, and was related to Gelfand’s spectrum of a Banach algebra. In the early 2000’s Reese Harvey and I found a projective analogue of these concepts and wondered whether Wermer’s Theorem could be generalized to the projective setting. This question turned out to be more subtle and quite intriguing\, with unexpected consequences. We now know a great deal\, a highpoint of which s a result with Harvey and Wermer. It led to conjectures (for Cω-curves in P2C) which imply several results. One says\, roughly\, that a (2p − 1)-cycle Γ in Pn bounds a positive holomorphic p-chain of mass ≤ Λ ⇐⇒ its normalized linking number with all positive (n − p)-cycles in Pn − |Γ| is ≥ −Λ. Another says that a class τ ∈ H2p(Pn\,|Γ|;Z) with ∂τ = Γ contains a positive holomorphic p-chain ⇐⇒ τ•[Z]≥0 for all positive holomorphic (n−p)-cycles Z in Pn−|Γ| \nVideo\n\n\n12:30–2:30 pm\nLunch Break\n\n\n\n2:30–3:30 pm\nGabor Szekelyhidi\nTitle: Singularities along the Lagrangian mean curvature flow. \nAbstract: We study singularity formation along the Lagrangian mean curvature flow of surfaces. On the one hand we show that if a tangent flow at a singularity is the special Lagrangian union of two transverse planes\, then the flow undergoes a “neck pinch”\, and can be continued past the flow. This can be related to the Thomas-Yau conjecture on stability conditions along the Lagrangian mean curvature flow. In a different direction we show that ancient solutions of the flow\, whose blow-down is given by two planes meeting along a line\, must be translators. These are joint works with Jason Lotay and Felix Schulze. \nVideo\n\n\n3:30–4:00 pm\nCoffee Break\n \n\n\n4:00–5:00 pm\nTakeo Ohsawa\nTitle: Glimpses of embeddings and deformations of CR manifolds \nAbstract: Basic results on the embeddings and the deformations of CR manifolds will be reviewed with emphasis on the reminiscences of impressive moments with Kuranishi since his visit to Kyoto in 1975. \nVideo\n\n\n\n  \n  \n  \nTuesday\, May 10\, 2022 \n  \n\n\n\n8:15 am\nLight breakfast & coffee/tea\n\n\n9:00–10:00 am\nCharles Fefferman (Zoom)\nTitle: Interpolation of Data by Smooth Functions \nAbstract: Let X be your favorite Banach space of continuous functions on R^n. Given an (arbitrary) set E in R^n and an arbitrary function f:E->R\, we ask: How can we tell whether f extends to a function F \in X? If such an F exists\, then how small can we take its norm? What can we say about its derivatives (assuming functions in X have derivatives)? Can we take F to depend linearly on f? Suppose E is finite. Can we compute an F as above with norm nearly as small as possible? How many computer operations does it take? What if F is required to agree only approximately with f on E? What if we are allowed to discard a few data points (x\, f(x)) as “outliers”? Which points should we discard? \nThe results were obtained jointly with A. Israel\, B. Klartag\, G.K. Luli and P. Shvartsman over many years. \nVideo\n\n\n10:15–11:15 am\nClaire Voisin\nTitle: Deformations of K-trivial manifolds and applications to hyper-Kähler geometry \nSummary: I will explain the Ran approach via the T^1-lifting principle to the BTT theorem stating that deformations of K-trivial compact Kähler manifolds are unobstructed. I will explain a similar unobstructedness result for Lagrangian submanifolds of hyper-Kähler manifolds and I will describe important consequences on the topology and geometry of hyper-Kähler manifolds. \nVideo\n\n\n11:30– 2:30 pm\nVictor Guillemin\nTitle: Semi-Classical Functions of Isotropic Type \nAbstract: The world of semiclassical analysis is populated by objects of “Lagrangian type.” The topic of this talk however will be objects in semi-classical analysis that live instead on isotropic submanifolds. I will describe in my talk a lot of interesting examples of such objects. \nVideo\n\n\n12:30–2:30 pm\nLunch Break\n\n\n\n2:30–3:30 pm\nTeng Fei\nTitle: Symplectic deformations and the Type IIA flow \nAbstract: The equations of flux compactification of Type IIA superstrings were written down by Tomasiello and Tseng-Yau. To study these equations\, we introduce a natural geometric flow known as the Type IIA flow on symplectic Calabi-Yau 6-manifolds. We prove the wellposedness of this flow and establish the basic estimates. We show that the Type IIA flow can be applied to find optimal almost complex structures on certain symplectic manifolds. We prove the dynamical stability of the Type IIA flow\, which leads to a proof of stability of Kahler property for Calabi-Yau 3-folds under symplectic deformations. This is based on joint work with Phong\, Picard and Zhang. \nVideo\n\n\nSpeakers Banquet\n\n\n\n\n\n  \n  \n  \nWednesday\, May 11\, 2022 \n  \n\n\n\n8:15 am\nLight breakfast & coffee/tea\n\n\n9:00–10:00 am\nShing-Tung Yau (Zoom)\nTitle: Canonical metrics and stability in mirror symmetry \nAbstract: I will discuss the deformed Hermitian-Yang-Mills equation\, its role in mirror symmetry and its connections to notions of stability.  I will review what is known\, and pose some questions for the future. \nVideo\n\n\n10:15–11:15 am\nDuong H. Phong\nTitle: $L^\infty$ estimates for the Monge-Ampere and other fully non-linear equations in complex geometry \nAbstract: A priori estimates are essential for the understanding of partial differential equations\, and of these\, $L^\infty$ estimates are particularly important as they are also needed for other estimates. The key $L^\infty$ estimates were obtained by S.T. Yau in 1976 for the Monge-Ampere equation for the Calabi conjecture\, and sharp estimates obtained later in 1998 by Kolodziej using pluripotential theory. It had been a long-standing question whether a PDE proof of these estimates was possible. We provide a positive answer to this question\, and derive as a consequence sharp estimates for general classes of fully non-linear equations. This is joint work with B. Guo and F. Tong. \nVideo\n\n\n11:30–2:30 pm\nPaul Seidel\nTitle: The quantum connection: familiar yet puzzling \nAbstract: The small quantum connection on a Fano variety is possibly the most basic piece of enumerative geometry. In spite of being really easy to write down\, it is the subject of far-reaching conjectures (Dubrovin\, Galkin\, Iritani)\, which challenge our understanding of mirror symmetry. I will give a gentle introduction to the simplest of these questions. \nVideo\n\n\n12:30–2:30 pm\nLunch Break\n\n\n\n2:30–3:30 pm\nMelissa C.C. Liu\nTitle: Higgs-Coulumb correspondence for abelian gauged linear sigma models \nAbstract: The underlying geometry of a gauged linear sigma model (GLSM) consists of a GIT quotient of a complex vector space by the linear action of a reductive algebraic group G (the gauge group) and a polynomial function (the superpotential) on the GIT quotient. The Higgs-Coulomb correspondence relates (1) GLSM invariants which are virtual counts of curves in the critical locus of the superpotential (Higgs branch)\, and (2) Mellin-Barnes type integrals on the Lie algebra of G (Coulomb branch). In this talk\, I will describe the correspondence when G is an algebraic torus\, and explain how to use the correspondence to study dependence of GLSM invariants on the stability condition. This is based on joint work with Konstantin Aleshkin. \nVideo\n\n\n3:30–4:00 pm\nCoffee Break\n \n\n\n4:00–5:00 pm\nSebastien Picard\nTitle: Topological Transitions of Calabi-Yau Threefolds \nAbstract: Conifold transitions were proposed in the works of Clemens\, Reid and Friedman as a way to travel in the parameter space of Calabi-Yau threefolds with different Hodge numbers. This process may deform a Kahler Calabi-Yau threefold into a non-Kahler complex manifold with trivial canonical bundle. We will discuss the propagation of differential geometric structures such as balanced hermitian metrics\, Yang-Mills connections\, and special submanifolds through conifold transitions. This is joint work with T. Collins\, S. Gukov and S.-T. Yau. \nVideo\n\n\n\n  \n  \n  \nThursday\, May 12\, 2022 \n  \n\n\n\n8:15 am\nLight breakfast & coffee/tea\n\n\n9:00 am–10:00 am\nAkito Futaki (Zoom)\nTitle: Transverse coupled Kähler-Einstein metrics and volume minimization\n\nAbstract: We show that transverse coupled Kähler-Einstein metrics on toric Sasaki manifolds arise as a critical point of a volume functional. As a preparation for the proof\, we re-visit the transverse moment polytopes and contact moment polytopes under the change of Reeb vector fields. Then we apply it to a coupled version of the volume minimization by Martelli-Sparks-Yau. This is done assuming the Calabi-Yau condition of the Kählercone\, and the non-coupled case leads to a known existence result of a transverse Kähler-Einstein metric and a Sasaki-Einstein metric\, but the coupled case requires an assumption related to Minkowski sum to obtain transverse coupled Kähler-Einstein metrics.Video\n\n\n10:15 am–11:15 am\nYu-Shen Lin\nTitle: SYZ Mirror Symmetry of Log Calabi-Yau Surfaces \nAbstract: Strominger-Yau-Zaslow conjecture predicts Calabi-Yau manifolds admits special Lagrangian fibrations. The conjecture serves as one of the guiding principles in mirror symmetry. In this talk\, I will explain the existence of the special Lagrangian fibrations in some log Calabi-Yau surfaces and their dual fibrations in their expected mirrors. The journey leads us to the study of the moduli space of Ricci-flat metrics with certain asymptotics on these geometries and the discovery of new semi-flat metrics. If time permits\, I will explain the application to the Torelli theorem of ALH^* gravitational instantons. The talk is based on joint works with T. Collins and A. Jacob. \nVideo\n\n\n11:30 am – 12:30 pm\nRobert Friedman\nTitle: Deformations of singular Fano and Calabi-Yau varieties \nAbstract: This talk will describe recent joint work with Radu Laza on deformations of generalized Fano and Calabi-Yau varieties\, i.e. compact analytic spaces whose dualizing sheaves are either duals of ample line bundles or are trivial. Under the assumption of isolated hypersurface canonical singularities\, we extend results of Namikawa and Steenbrink in dimension three and discuss various generalizations to higher dimensions. \nVideo\n\n\n12:30 pm\nConcluding Remarks\n\n\n\n 
URL:https://cmsa.fas.harvard.edu/event/conference-in-memory-of-professor-masatake-kuranishi/
LOCATION:Science and Engineering Complex (SEC)\, 150 Western Ave\, Allston\, MA 02134\, MA
CATEGORIES:Conference,Event
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Kuranishi_Harvard_10x12-2.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220509T130000
DTEND;TZID=America/New_York:20220509T140000
DTSTAMP:20260502T192358
CREATED:20230730T181939Z
LAST-MODIFIED:20240214T102113Z
UID:10001150-1652101200-1652104800@cmsa.fas.harvard.edu
SUMMARY:Inflation and light Dark Matter constraints from the Swampland
DESCRIPTION:Abstract: I will explore the interplay between Swampland conjectures and models of inflation and light Dark Matter. To that end\, I will briefly review the weak gravity conjecture (WGC) and the related Festina Lente (FL) bound. These have implications for light darkly and milli-charged particles and can disfavor a large portion of parameter space. The FL bound also implies strong restrictions on the field content of our universe during inflation and presents an opportunity for inflationary model building. At the same time\, it rules out some popular models like chromo-natural inflation and gauge-flation. Finally\, I will review  another Swampland conjecture related to Stückelberg photon masses and discuss its implications for astro-particle physics.
URL:https://cmsa.fas.harvard.edu/event/5-9-2022-swampland-seminar/
LOCATION:Virtual
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220511T103000
DTEND;TZID=America/New_York:20220511T120000
DTSTAMP:20260502T192358
CREATED:20240214T100851Z
LAST-MODIFIED:20240813T163022Z
UID:10002659-1652265000-1652270400@cmsa.fas.harvard.edu
SUMMARY:Cosmology from the vacuum
DESCRIPTION:Abstract: We are familiar with the idea that quantum gravity in AdS can holographically emerge from complex patterns of entanglement\, but can the physics of big bang cosmology emerge from a quantum many-body system? In this talk I will argue that standard tools of holography can be used to describe fully non-perturbative microscopic models of cosmology in which a period of accelerated expansion may result from the positive potential energy of time-dependent scalar fields evolving towards a region with negative potential. In these models\, the fundamental cosmological constant is negative\, and the universe eventually recollapses in a time-reversal symmetric way. The microscopic description naturally selects a special state for the cosmology. In this framework\, physics in the cosmological spacetime is dual to the vacuum physics in a static planar asymptotically AdS Lorentzian wormhole spacetime\, in the sense that the background spacetimes and observables are related by analytic continuation. The dual spacetime is weakly curved everywhere\, so any cosmological observables can be computed in the dual picture via effective field theory without detailed knowledge of the UV completion or the physics near the big bang. Based on 2203.11220 with S. Antonini\, P. Simidzija\, and M. Van Raamsdonk.
URL:https://cmsa.fas.harvard.edu/event/5-11-2022-quantum-matter-in-mathematics-and-physics/
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-Seminar-05.11.22-1583x2048-1.png
END:VEVENT
END:VCALENDAR