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DTSTART;TZID=America/New_York:20210913T090000
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DTSTAMP:20260503T143214
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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:20260503T143214
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
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220124T090000
DTEND;TZID=America/New_York:20220521T170000
DTSTAMP:20260503T143214
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:20260503T143214
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
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220315T090000
DTEND;TZID=America/New_York:20220315T100000
DTSTAMP:20260503T143214
CREATED:20240214T065321Z
LAST-MODIFIED:20240304T085303Z
UID:10002551-1647334800-1647338400@cmsa.fas.harvard.edu
SUMMARY:Moduli space of tropical curves\, graph Laplacians and physics
DESCRIPTION:Abstract: I will first review the construction of the moduli space of tropical curves (or metric graphs)\, and its relation to graph complexes. The graph Laplacian may be interpreted as a tropical version of the classical Torelli map and its determinant is the Kirchhoff graph polynomial (also called 1st Symanzik)\, which is one of the two key components in Feynman integrals in high energy physics.The other component is the so-called 2nd Symanzik polynomial\, which is defined for graphs with external half edges and involves particle masses (edge colourings). I will explain how this too may be interpreted as the determinant of a generalised graph Laplacian\, and how it leads to a volumetric interpretation of a certain class of Feynman integrals.
URL:https://cmsa.fas.harvard.edu/event/3-15-2022-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-3.15.2022-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220315T093000
DTEND;TZID=America/New_York:20220315T103000
DTSTAMP:20260503T143214
CREATED:20230825T075742Z
LAST-MODIFIED:20240304T082952Z
UID:10001292-1647336600-1647340200@cmsa.fas.harvard.edu
SUMMARY:2-categorical 3d mirror symmetry
DESCRIPTION:Abstract: It is by now well-known that mirror symmetry may be expressed as an equivalence between categories associated to dual Kahler manifolds. Following a proposal of Teleman\, we inaugurate a program to understand 3d mirror symmetry as an equivalence between 2-categories associated to dual holomorphic symplectic stacks. We consider here the abelian case\, where our theorem expresses the 2-category of spherical functors as a 2-category of coherent sheaves of categories. Applications include categorifications of hypertoric category O and of many related constructions in representation theory. This is joint work with Justin Hilburn and Aaron Mazel-Gee.
URL:https://cmsa.fas.harvard.edu/event/2-categorical-3d-mirror-symmetry/
LOCATION:Virtual
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220315T100000
DTEND;TZID=America/New_York:20220315T230000
DTSTAMP:20260503T143214
CREATED:20240214T092307Z
LAST-MODIFIED:20240301T113301Z
UID:10002622-1647338400-1647385200@cmsa.fas.harvard.edu
SUMMARY:Birkhoff’s conjecture on integrable billiards and Kac’s problem “hearing the shape of a drum”
DESCRIPTION:Abstract: Billiards on an elliptical billiard table are completely integrable: phase space is foliated by invariant submanifolds for the billiard flow. Birkhoff conjectured that ellipses are the only plane domains with integrable billiards. Avila-deSimoi- Kaloshin proved the conjecture for ellipses of sufficiently small eccentricity. Kaloshin-Sorrentino proved local results for all eccentricities. On the quantum level\, the analogous conjecture is that ellipses are uniquely determined by their Dirichlet (or\, Neumann) eigenvalues. Using the results on the Birkhoff conjecture\, Hamid Hezari and I proved that for ellipses of small eccentricity are indeed uniquely determined by their eigenvalues. Except for disks\, which Kac proved to be uniquely determined\, these are the only domains for which it is known that one can hear their shape.
URL:https://cmsa.fas.harvard.edu/event/3-15-2022-joint-harvard-cuhk-ymsc-differential-geometry-seminar/
CATEGORIES:Joint Harvard-CUHK-YMSC Differential Geometry
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220316T103000
DTEND;TZID=America/New_York:20220316T120000
DTSTAMP:20260503T143214
CREATED:20240214T104642Z
LAST-MODIFIED:20240301T065907Z
UID:10002679-1647426600-1647432000@cmsa.fas.harvard.edu
SUMMARY:Summing Over Bordisms In 2d TQFT
DESCRIPTION:Abstract: Some recent work in the quantum gravity literature has considered what happens when the amplitudes of a TQFT are summed over the bordisms between fixed in-going and out-going boundaries. We will comment on these constructions. The total amplitude\, that takes into account all in-going and out-going boundaries can be presented in a curious factorized form. This talk reports on work done with Anindya Banerjee and is based on the paper on the e-print arXiv  2201.00903.
URL:https://cmsa.fas.harvard.edu/event/3-16-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-03.16.2022-1544x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220317T093000
DTEND;TZID=America/New_York:20220317T110000
DTSTAMP:20260503T143214
CREATED:20240214T104122Z
LAST-MODIFIED:20240813T163816Z
UID:10002678-1647509400-1647514800@cmsa.fas.harvard.edu
SUMMARY: A Hike through the Swampland
DESCRIPTION:Abstract: The Swampland program aims at uncovering the universal implications of quantum gravity at low-energy physics. I will review the basic ideas of the Swampland program\, formal and phenomenological implications\, and provide a survey of the techniques commonly used in Swampland research including tools from quantum information\, holography\, supersymmetry\, and string theory.
URL:https://cmsa.fas.harvard.edu/event/3-17-2022-quantum-matter-in-mathematics-and-physics/
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-03.17.2022-1-1544x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220317T151500
DTEND;TZID=America/New_York:20220317T161500
DTSTAMP:20260503T143214
CREATED:20240215T091301Z
LAST-MODIFIED:20240301T104445Z
UID:10002709-1647530100-1647533700@cmsa.fas.harvard.edu
SUMMARY:On optimization and generalization in deep learning
DESCRIPTION:Abstract: Deep neural networks have achieved significant empirical success in many fields\, including the fields of computer vision and natural language processing. Along with its empirical success\, deep learning has been theoretically shown to be attractive in terms of its expressive power. However\, the theory of expressive power does not ensure that we can efficiently find an optimal solution in terms of optimization and generalization\, during the optimization process. In this talk\, I will discuss some mathematical properties of optimization and generalization for deep neural networks.
URL:https://cmsa.fas.harvard.edu/event/3-17-2022-interdisciplinary-science-seminar/
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-03.17.2022-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220318T093000
DTEND;TZID=America/New_York:20220318T103000
DTSTAMP:20260503T143214
CREATED:20240214T084936Z
LAST-MODIFIED:20240301T111106Z
UID:10002599-1647595800-1647599400@cmsa.fas.harvard.edu
SUMMARY:Moduli Space of Metric SUSY Graphs
DESCRIPTION:Member Seminar \nSpeaker: Yingying Wu \nTitle: Moduli Space of Metric SUSY Graphs \nAbstract: SUSY curves are algebraic curves with additional supersymmetric or supergeometric structures. In this talk\, I will present the construction of dual graphs of SUSY curves with Neveu–Schwarz and Ramond punctures. Then\, I will introduce the concept of the metrized SUSY graph and the moduli space of the metric SUSY graphs. I will outline its geometric and topological properties\, followed by a discussion on the connection with the classical case.
URL:https://cmsa.fas.harvard.edu/event/3-18-2022-member-seminar/
LOCATION:Virtual
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220321T130000
DTEND;TZID=America/New_York:20220321T140000
DTSTAMP:20260503T143214
CREATED:20230730T180020Z
LAST-MODIFIED:20240301T073804Z
UID:10001145-1647867600-1647871200@cmsa.fas.harvard.edu
SUMMARY:3/21/2022 – Swampland Seminar
DESCRIPTION:Open Mic Discussion\nTopic: Entropy bounds (species bound\, Bekenstein bound\, CKN bound\, and the like)
URL:https://cmsa.fas.harvard.edu/event/3-21-2022-swampland-seminar/
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220321T130000
DTEND;TZID=America/New_York:20220321T140000
DTSTAMP:20260503T143214
CREATED:20240214T081657Z
LAST-MODIFIED:20240813T160939Z
UID:10002584-1647867600-1647871200@cmsa.fas.harvard.edu
SUMMARY:Bulk-boundary correspondence for vacuum asymptotically Anti-de Sitter spacetimes
DESCRIPTION:Abstract: The AdS/CFT conjecture in physics posits the existence of a correspondence between gravitational theories in asymptotically Anti-de Sitter (aAdS) spacetimes and field theories on their conformal boundary. In this presentation\, we prove rigorous mathematical statements toward this conjecture. \nIn particular\, we show there is a one-to-one correspondence between aAdS solutions of the Einstein-vacuum equations and a suitable space of data on the conformal boundary (consisting of the boundary metric and the boundary stress-energy tensor). We also discuss consequences of this result\, as well as the main ingredient behind its proof: a unique continuation property for wave equations on aAdS spacetimes. \nThis is joint work with Gustav Holzegel (and makes use of joint works with Alex McGill and Athanasios Chatzikaleas).
URL:https://cmsa.fas.harvard.edu/event/3-21-2022-general-relativity-seminar/
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-03.21.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220322T093000
DTEND;TZID=America/New_York:20220322T103000
DTSTAMP:20260503T143214
CREATED:20240214T065544Z
LAST-MODIFIED:20240304T085053Z
UID:10002552-1647941400-1647945000@cmsa.fas.harvard.edu
SUMMARY:Flip processes
DESCRIPTION:Abstract: We introduce a class of random graph processes\, which we call \emph{flip processes}. Each such process is given by a \emph{rule} which is just a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all labelled $k$-vertex graphs into itself ($k$ is fixed). The process starts with a given $n$-vertex graph $G_0$. In each step\, the graph $G_i$ is obtained by sampling $k$ random vertices $v_1\,\ldots\,v_k$ of $G_{i-1}$ and replacing the induced graph $F:=G_{i-1}[v_1\,\ldots\,v_k]$ by  $\mathcal{R}(F)$. This class contains several previously studied processes including the Erd\H{o}s–R\’enyi random graph process and the triangle removal process. \nGiven a flip process with a rule $\mathcal{R}$\, we construct time-indexed trajectories $\Phi:\Gra\times [0\,\infty)\rightarrow\Gra$ in the space of graphons. We prove that for any $T > 0$ starting with a large finite graph $G_0$ which is close to a graphon $W_0$ in the cut norm\, with high probability the flip process will stay in a thin sausage around the trajectory $(\Phi(W_0\,t))_{t=0}^T$ (after rescaling the time by the square of the order of the graph). \nThese graphon trajectories are then studied from the perspective of dynamical systems. Among others\, we study continuity properties of these trajectories with respect to time and the initial graphon\, existence and stability of fixed points and speed of convergence (whenever the infinite time limit exists). We give an example of a flip process with a periodic trajectory. This is joint work with Frederik Garbe\, Matas \v Sileikis and Fiona Skerman (arXiv:2201.12272). \nWe also study several specific families flip processes. This is joint work with Pedro Ara\’ujo\, Eng Keat Hng and Matas \v{S}ileikis (in preparation).\nA brief introduction to the necessary bits of the theory of graph limits will be given in the talk.
URL:https://cmsa.fas.harvard.edu/event/3-22-2022-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-3.15.2022-1-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220323T093000
DTEND;TZID=America/New_York:20220323T103000
DTSTAMP:20260503T143214
CREATED:20240214T040105Z
LAST-MODIFIED:20240507T192932Z
UID:10002519-1648027800-1648031400@cmsa.fas.harvard.edu
SUMMARY:Fluctuation scaling or Taylor’s law of heavy-tailed data\, illustrated by U.S. COVID-19 cases and deaths
DESCRIPTION:Speaker: Joel E. Cohen (Rockefeller University and Columbia University) \nTitle: Fluctuation scaling or Taylor’s law of heavy-tailed data\, illustrated by U.S. COVID-19 cases and deaths \nAbstract: Over the last century\, ecologists\, statisticians\, physicists\, financial quants\, and other scientists discovered that\, in many examples\, the sample variance approximates a power of the sample mean of each of a set of samples of nonnegative quantities. This power-law relationship of variance to mean is known as a power variance function in statistics\, as Taylor’s law in ecology\, and as fluctuation scaling in physics and financial mathematics. This survey talk will emphasize ideas\, motivations\, recent theoretical results\, and applications rather than detailed proofs. Many models intended to explain Taylor’s law assume the probability distribution underlying each sample has finite mean and variance. Recently\, colleagues and I generalized Taylor’s law to samples from probability distributions with infinite mean or infinite variance and higher moments. For such heavy-tailed distributions\, we extended Taylor’s law to higher moments than the mean and variance and to upper and lower semivariances (measures of upside and downside portfolio risk). In unpublished work\, we suggest that U.S. COVID-19 cases and deaths illustrate Taylor’s law arising from a distribution with finite mean and infinite variance. This model has practical implications. Collaborators in this work are Mark Brown\, Richard A. Davis\, Victor de la Peña\, Gennady Samorodnitsky\, Chuan-Fa Tang\, and Sheung Chi Phillip Yam.
URL:https://cmsa.fas.harvard.edu/event/colloquium_32223/
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-03.23.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220323T103000
DTEND;TZID=America/New_York:20220323T120000
DTSTAMP:20260503T143214
CREATED:20240214T103754Z
LAST-MODIFIED:20240301T064719Z
UID:10002677-1648031400-1648036800@cmsa.fas.harvard.edu
SUMMARY:Non-zero momentum requires long-range entanglement
DESCRIPTION:Youtube Video \n  \nAbstract: I will show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum\, i.e. if it is an eigenstate of the translation symmetry with eigenvalue not equal to 1. Equivalently\, any state that can be connected with a non-zero momentum state through a finite-depth local unitary transformation must also be long-range entangled. The statement can also be generalized to fermion systems. I will then present two applications of this result: (1) several different types of Lieb-Schultz-Mattis (LSM) theorems\, including a previously unknown version involving only a discrete Z_n symmetry\, can be derived in a simple manner; (2) a gapped topological order (in space dimension d>1) must weakly break translation symmetry if one of its ground states on torus has nontrivial momentum – this generalizes the familiar physics of Tao-Thouless in fractional quantum Hall systems.
URL:https://cmsa.fas.harvard.edu/event/3-23-2022-quantum-matter-in-mathematics-and-physics/
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-03.23.2022-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220323T140000
DTEND;TZID=America/New_York:20220323T150000
DTSTAMP:20260503T143214
CREATED:20230808T183247Z
LAST-MODIFIED:20240515T202339Z
UID:10001208-1648044000-1648047600@cmsa.fas.harvard.edu
SUMMARY:Formal Mathematics Statement Curriculum Learning
DESCRIPTION:Speaker: Stanislas Polu\, OpenAI \nTitle: Formal Mathematics Statement Curriculum Learning \nAbstract: We explore the use of expert iteration in the context of language modeling applied to formal mathematics. We show that at same compute budget\, expert iteration\, by which we mean proof search interleaved with learning\, dramatically outperforms proof search only.  We also observe that when applied to a collection of formal statements of sufficiently varied difficulty\, expert iteration is capable of finding and solving a curriculum of increasingly difficult problems\,  without the need for associated ground-truth proofs. Finally\, by applying this expert iteration to a manually curated set of problem statements\, we achieve state-of-the-art on the miniF2F benchmark\,  automatically solving multiple challenging problems drawn from high school olympiads.
URL:https://cmsa.fas.harvard.edu/event/3-23-2022-new-technologies-in-mathematics-seminar/
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-03.23.2022-1553x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220324T093000
DTEND;TZID=America/New_York:20220324T103000
DTSTAMP:20260503T143214
CREATED:20240214T082228Z
LAST-MODIFIED:20240301T113314Z
UID:10002585-1648114200-1648117800@cmsa.fas.harvard.edu
SUMMARY:Rough solutions of the $3$-D compressible Euler equations
DESCRIPTION:Abstract: I will talk about my work on the compressible Euler equations. We prove the local-in-time existence the solution of the compressible Euler equations in $3$-D\, for the Cauchy data of the velocity\, density and vorticity $(v\,\varrho\, \omega) \in H^s\times H^s\times H^{s’}$\, $2<s'<s$.  The result extends the sharp result of Smith-Tataru and Wang\, established in the irrotational case\, i.e $\omega=0$\, which is known to be optimal for $s>2$. At the opposite extreme\, in the incompressible case\, i.e. with a constant density\,  the result is known to hold for $\omega\in H^s$\, $s>3/2$ and fails for $s\le 3/2$\, see the work of Bourgain-Li. It is thus natural to conjecture that the optimal result should be  $(v\,\varrho\, \omega) \in H^s\times H^s\times H^{s’}$\, $s>2\, \\, s’>\frac{3}{2}$. We view our work as an important step in proving the conjecture. The main difficulty in establishing sharp well-posedness results for general compressible Euler flow is due to the highly nontrivial interaction between the sound waves\, governed by quasilinear wave equations\, and vorticity which is transported by the flow. To overcome this difficulty\, we separate the dispersive part of a sound wave from the transported part and gain regularity significantly by exploiting the nonlinear structure of the system and the geometric structures of the acoustic spacetime.
URL:https://cmsa.fas.harvard.edu/event/3-24-2022-general-relativity-seminar/
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-03.24.22-2.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220324T093000
DTEND;TZID=America/New_York:20220324T110000
DTSTAMP:20260503T143214
CREATED:20240214T103248Z
LAST-MODIFIED:20240813T162724Z
UID:10002675-1648114200-1648119600@cmsa.fas.harvard.edu
SUMMARY:Edge physics at the deconfined transition between a quantum spin Hall insulator and a superconductor
DESCRIPTION:Youtube Video \n  \nAbstract: I will talk about the edge physics of the deconfined quantum phase transition (DQCP) between a spontaneous quantum spin Hall (QSH) insulator and a spin-singlet superconductor (SC). Although the bulk of this transition is in the same universality class as the paradigmatic deconfined Neel to valence-bond-solid transition\, the boundary physics has a richer structure due to proximity to a quantum spin Hall state. We use the parton trick to write down an effective field theory for the QSH-SC transition in the presence of a boundary and calculate various edge properties in a large-N limit. We show that the boundary Luttinger liquid in the QSH state survives at the phase transition\, but only as fractional degrees of freedom that carry charge but not spin. The physical fermion remains gapless on the edge at the critical point\, with a universal jump in the fermion scaling dimension as the system approaches the transition from the QSH side. The critical point could be viewed as a gapless analogue of the QSH state but with the full SU(2) spin rotation symmetry\, which cannot be realized if the bulk is gapped. This talk reports on the work done with Liujun Zou and Chong Wang (arxiv:2110.08280).
URL:https://cmsa.fas.harvard.edu/event/3-24-2022-quantum-matter-in-mathematics-and-physics/
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-03.24.2022-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220324T130000
DTEND;TZID=America/New_York:20220324T142000
DTSTAMP:20260503T143214
CREATED:20230824T173250Z
LAST-MODIFIED:20240122T085257Z
UID:10001309-1648126800-1648131600@cmsa.fas.harvard.edu
SUMMARY:Topological defects drive layer formation in gliding bacteria colonies
DESCRIPTION:Abstract: The developmental cycle of Myxococcus xanthus involves the coordination of many hundreds of thousands of cells aggregating to form mounds known as fruiting bodies. This aggregation process begins with the sequential formation of more and more cell layers. Using three-dimensional confocal imaging we study this layer formation process by observing the formation of holes and second layers within a base monolayer of M xanthus cells. We find that cells align with each other over the majority of the monolayer forming an active nematic liquid crystal with defect point where cell alignment is undefined. We find that new layers and holes form at positive and negative topological defects respectively. We model the cell layer using hydrodynamic modeling and find that this layer and hole formation process is driven by active nematic forces through cell motility and anisotropic substrate friction.
URL:https://cmsa.fas.harvard.edu/event/topological-defects-drive-layer-formation-in-gliding-bacteria-colonies/
LOCATION:Virtual
CATEGORIES:Active Matter Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Active-Matter-Seminar-03.24.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220324T151700
DTEND;TZID=America/New_York:20220324T171700
DTSTAMP:20260503T143214
CREATED:20240215T091039Z
LAST-MODIFIED:20240301T104333Z
UID:10002708-1648135020-1648142220@cmsa.fas.harvard.edu
SUMMARY:An operadic structure on supermoduli spaces
DESCRIPTION:Abstract: The operadic structure on the moduli spaces of algebraic curves  encodes in a combinatorial way how nodal curves in the boundary can be obtained by glueing smooth curves along marked points. In this talk\, I will present a generalization of the operadic structure to moduli spaces of SUSY curves (or super Riemann surfaces). This requires colored graphs and generalized operads in the sense of Borisov-Manin. Based joint work with Yu. I. Manin and Y. Wu. https://arxiv.org/abs/2202.10321
URL:https://cmsa.fas.harvard.edu/event/3-24-2022-interdisciplinary-science-seminar/
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-03.24.2022-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220325T093000
DTEND;TZID=America/New_York:20220325T103000
DTSTAMP:20260503T143214
CREATED:20240214T084728Z
LAST-MODIFIED:20240301T110538Z
UID:10002597-1648200600-1648204200@cmsa.fas.harvard.edu
SUMMARY:Periods for singular CY families and Riemann–Hilbert correspondence
DESCRIPTION:Member Seminar \nSpeaker: Tsung-Ju Lee \nTitle: Periods for singular CY families and Riemann–Hilbert correspondence \nAbstract: A GKZ system\, introduced by Gelfand\, Kapranov\, and Zelevinsky\, is a system of partial differential equations generalizing the hypergeometric structure studied by Euler and Gauss. The solutions to GKZ systems have been found applications in various branches of mathematics including number theory\, algebraic geometry and mirror symmetry. In this talk\, I will explain the details and demonstrate how to find the Riemann–Hilbert partner of the GKZ system with a fractional parameter which arises from the B model of singular CY varieties. This is a joint work with Dingxin Zhang.
URL:https://cmsa.fas.harvard.edu/event/3-25-2022-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220328T130000
DTEND;TZID=America/New_York:20220328T140000
DTSTAMP:20260503T143214
CREATED:20230730T180327Z
LAST-MODIFIED:20240301T070636Z
UID:10001146-1648472400-1648476000@cmsa.fas.harvard.edu
SUMMARY:On renormalisation group induced moduli stabilisation and brane-antibrane inflation
DESCRIPTION:Abstract: A proposal to use the renormalisation group to address moduli stabilisation in IIB string perturbation theory will be described. We revisit brane-antibrane inflation combining this proposal with non-linearly realised supersymmetry.
URL:https://cmsa.fas.harvard.edu/event/3-28-2022-swampland-seminar-series/
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220328T130000
DTEND;TZID=America/New_York:20220328T140000
DTSTAMP:20260503T143214
CREATED:20240214T082503Z
LAST-MODIFIED:20240301T113123Z
UID:10002586-1648472400-1648476000@cmsa.fas.harvard.edu
SUMMARY:Black Hole Spectroscopy
DESCRIPTION:Abstract: According to general relativity\, the remnant of a binary black hole merger should be a perturbed Kerr black hole. Perturbed Kerr black holes emit “ringdown” radiation which is well described by a superposition of quasinormal modes\, with frequencies and damping times that depend only on the mass and spin of the remnant. Therefore the observation of gravitational radiation emitted by black hole mergers might finally provide direct evidence of black holes with the same certainty as\, say\, the 21 cm line identifies interstellar hydrogen. I will review the current status of this “black hole spectroscopy” program. I will focus on two important open issues: (1) When is the waveform well described by linear black hole perturbation theory? (2) What is the current observational status of black hole spectroscopy?
URL:https://cmsa.fas.harvard.edu/event/3-28-2022-general-relativity-seminar/
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220329T090000
DTEND;TZID=America/New_York:20220329T100000
DTSTAMP:20260503T143214
CREATED:20240213T110525Z
LAST-MODIFIED:20240304T102009Z
UID:10002473-1648544400-1648548000@cmsa.fas.harvard.edu
SUMMARY:Combinatorics\, Physics and Probability Seminar
DESCRIPTION:During the 2021–22 academic year\, the CMSA will be hosting a seminar on Combinatorics\, Physics and Probability\, organized by Matteo Parisi and Michael Simkin. This seminar will take place on Tuesdays at 9:00 am – 10:00 am (Boston time). The meetings will take place virtually on Zoom. To learn how to attend\, please fill out this form\, or contact the organizers Matteo (mparisi@cmsa.fas.harvard.edu) and Michael (msimkin@cmsa.fas.harvard.edu). \nThe schedule below will be updated as talks are confirmed. \nSpring 2022\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n1/25/2022\n*note special time 9:00–10:00 AM ET\nJacob Bourjaily (Penn State University\, Eberly College of Science\nTitle: Adventures in Perturbation Theory \nAbstract: Recent years have seen tremendous advances in our understanding of perturbative quantum field theory—fueled largely by discoveries (and eventual explanations and exploitation) of shocking simplicity in the mathematical form of the predictions made for experiment. Among the most important frontiers in this progress is the understanding of loop amplitudes—their mathematical form\, underlying geometric structure\, and how best to manifest the physical properties of finite observables in general quantum field theories. This work is motivated in part by the desire to simplify the difficult work of doing Feynman integrals. I review some of the examples of this progress\, and describe some ongoing efforts to recast perturbation theory in terms that expose as much simplicity (and as much physics) as possible.\n\n\n2/3/2022\nRan Tessler\n(Weizmann Institute of Science)\nTitle: The Amplituhedron BCFW Triangulation \nAbstract:  The (tree) amplituhedron was introduced in 2013 by Arkani-Hamed and Trnka in their study of N=4 SYM scattering amplitudes. A central conjecture in the field was to prove that the m=4 amplituhedron is triangulated by the images of certain positroid cells\, called the BCFW cells. In this talk I will describe a resolution of this conjecture. The seminar is based on a recent joint work with Chaim Even-Zohar and Tsviqa Lakrec.\n\n\n2/8/2022\nAnna Seigal (Harvard)\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\n2/15/2022\nIgor Balla\, Hebrew University of Jerusalem\nTitle: Equiangular lines and regular graphs \nAbstract: In 1973\, Lemmens and Seidel asked to determine N_alpha(r)\, the maximum number of equiangular lines in R^r with common angle arccos(alpha). Recently\, this problem has been almost completely settled when r is exponentially large relative to 1/alpha\, with the approach both relying on Ramsey’s theorem\, as well as being limited by it. In this talk\, we will show how orthogonal projections of matrices with respect to the Frobenius inner product can be used to overcome this limitation\, thereby obtaining significantly improved upper bounds on N_alpha(r) when r is polynomial in 1/alpha. In particular\, our results imply that N_alpha(r) = Theta(r) for alpha >= Omega(1 / r^1/5). \nOur projection method generalizes to complex equiangular lines in C^r\, which may be of independent interest in quantum theory. Applying this method also allows us to obtain\nthe first universal bound on the maximum number of complex equiangular lines in C^r with common Hermitian angle arccos(alpha)\, an extension of the Alon-Boppana theorem to dense regular graphs\, which is tight for strongly regular graphs corresponding to r(r+1)/2 equiangular lines in R^r\, an improvement to Welch’s bound in coding theory.\n\n\n\n\nFall 2021\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n9/21/2021\nNima Arkani-Hamed\nIAS (Institute for Advanced Study)\, School of Natural Sciences\nTitle: Surfacehedra and the Binary Positive Geometry of Particle and “String” Amplitudes\n\n\n9/28/2021\nMelissa Sherman-Bennett\nUniversity of Michigan\, Department of Mathematics\nTitle: The hypersimplex and the m=2 amplituhedron \nAbstract: I’ll discuss a 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). Along the way\, we prove the sign-flip 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 hypersimplex decomposition).\n\n\n10/5/2021\nDaniel Cizma\, Hebrew University\nTitle: Geodesic Geometry on Graphs \nAbstract: In a graph G = (V\, E) we consider a system of paths S so that for every two vertices u\,v in V there is a unique uv path in S connecting them. The path system is said to be consistent if it is closed under taking subpaths\, i.e. if P is a path in S then any subpath of P is also in S. Every positive weight function w: E–>R^+ gives rise to a consistent path system in G by taking the paths in S to be geodesics w.r.t. w. In this case\, we say w induces S. We say a graph G is metrizable if every consistent path system in G is induced by some such w. \nWe’ll discuss the concept of graph metrizability\, and\, in particular\, we’ll see that while metrizability is a rare property\, there exists infinitely many 2-connected metrizable graphs. \nJoint work with Nati Linial.\n\n\n10/12/2021\nLisa Sauermann\, MIT\nTitle: On counting algebraically defined graphs \nAbstract: For many classes of graphs that arise naturally in discrete geometry (for example intersection graphs of segments or disks in the plane)\, the edges of these graphs can be defined algebraically using the signs of a finite list of fixed polynomials. We investigate the number of n-vertex graphs in such an algebraically defined class of graphs. Warren’s theorem (a variant of a theorem of Milnor and Thom) implies upper bounds for the number of n-vertex graphs in such graph classes\, but all the previously known lower bounds were obtained from ad hoc constructions for very specific classes. We prove a general theorem giving a lower bound for this number (under some reasonable assumptions on the fixed list of polynomials)\, and this lower bound essentially matches the upper bound from Warren’s theorem.\n\n\n10/19/2021\nPavel Galashin\nUCLA\, Department of Mathematics\nTitle: Ising model\, total positivity\, and criticality \nAbstract: The Ising model\, introduced in 1920\, is one of the most well-studied models in statistical mechanics. It is known to undergo a phase transition at critical temperature\, and has attracted considerable interest over the last two decades due to special properties of its scaling limit at criticality.\nThe totally nonnegative Grassmannian is a subset of the real Grassmannian introduced by Postnikov in 2006. It arises naturally in Lusztig’s theory of total positivity and canonical bases\, and is closely related to cluster algebras and scattering amplitudes.\nI will give some background on the above objects and then explain a precise relationship between the planar Ising model and the totally nonnegative Grassmannian\, obtained in our recent work with P. Pylyavskyy. Building on this connection\, I will give a new boundary correlation formula for the critical Ising model.\n\n\n10/26/2021\nCandida Bowtell\, University of Oxford\nTitle: The n-queens problem \nAbstract: The n-queens problem asks how many ways there are to place n queens on an n x n chessboard so that no two queens can attack one another\, and the toroidal n-queens problem asks the same question where the board is considered on the surface of a torus. Let Q(n) denote the number of n-queens configurations on the classical board and T(n) the number of toroidal n-queens configurations. The toroidal problem was first studied in 1918 by Pólya who showed that T(n)>0 if and only if n is not divisible by 2 or 3. Much more recently Luria showed that T(n) is at most ((1+o(1))ne^{-3})^n and conjectured equality when n is not divisible by 2 or 3. We prove this conjecture\, prior to which no non-trivial lower bounds were known to hold for all (sufficiently large) n not divisible by 2 or 3. We also show that Q(n) is at least ((1+o(1))ne^{-3})^n for all natural numbers n which was independently proved by Luria and Simkin and\, combined with our toroidal result\, completely settles a conjecture of Rivin\, Vardi and Zimmerman regarding both Q(n) and T(n). \nIn this talk we’ll discuss our methods used to prove these results. A crucial element of this is translating the problem to one of counting matchings in a 4-partite 4-uniform hypergraph. Our strategy combines a random greedy algorithm to count `almost’ configurations with a complex absorbing strategy that uses ideas from the methods of randomised algebraic construction and iterative absorption. \nThis is joint work with Peter Keevash.\n\n\n11/9/2021\nSteven Karp\nUniversite du Quebec a Montreal\, LaCIM (Laboratoire de combinatoire et d’informatique mathématique)\nTitle: Gradient flows on totally nonnegative flag varieties\n\nAbstract: One can view a partial flag variety in C^n as an adjoint orbit inside the Lie algebra of n x n skew-Hermitian matrices. We use the orbit context to study the totally nonnegative part of a partial flag variety from an algebraic\, geometric\, and dynamical perspective. We classify gradient flows on adjoint orbits in various metrics which are compatible with total positivity. As applications\, we show how the classical Toda flow fits into this framework\, and prove that a new family of amplituhedra are homeomorphic to closed balls. This is joint work with Anthony Bloch.\n\n\n11/16/2021\n*note special time 12:30–1:30 ET*\nYinon Spinka (University of British Columbia)\nTitle: A tale of two balloons \nAbstract: From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch\, they pop and disappear. Will balloons reach the origin infinitely often or not? We answer this question for various underlying spaces. En route we find a new(ish) 0-1 law\, and generalize bounds on independent sets that are factors of IID on trees.\nJoint work with Omer Angel and Gourab Ray.\n\n\n11/23/2021\nLutz Warnke (UC San Diego)\nTitle: Prague dimension of random graphs \nAbstract: The Prague dimension of graphs was introduced by Nesetril\, Pultr and Rodl in the 1970s: as a combinatorial measure of complexity\, it is closely related to clique edges coverings and partitions. Proving a conjecture of Furedi and Kantor\, we show that the Prague dimension of the binomial random graph is typically of order n/(log n) for constant edge-probabilities. The main new proof ingredient is a Pippenger-Spencer type edge-coloring result for random hypergraphs with large uniformities\, i.e.\, edges of size O(log n).\n\n\n11/30/2021\nKarel Devriendt (University of Oxford)\nTitle: Resistance curvature – a new discrete curvature on graphs \nAbstract: The last few decades have seen a surge of interest in building towards a theory of discrete curvature that attempts to translate the key properties of curvature in differential geometry to the setting of discrete objects and spaces. In the case of graphs there have been several successful proposals\, for instance by Lin-Lu-Yau\, Forman and Ollivier\, that replicate important curvature theorems and have inspired applications in a variety of practical settings.\nIn this talk\, I will introduce a new notion of discrete curvature on graphs\, which we call the resistance curvature\, and discuss some of its basic properties. The resistance curvature is defined based on the concept of effective resistance which is a metric between the vertices of a graph and has many other properties such as a close relation to random spanning trees. The rich theory of these effective resistances allows to study the resistance curvature in great detail; I will for instance show that “Lin-Lu-Yau >= resistance >= Forman curvature” in a specific sense\, show strong evidence that the resistance curvature converges to zero in expectation for Euclidean random graphs\, and give a connectivity theorem for positively curved graphs. The resistance curvature also has a naturally associated discrete Ricci flow which is a gradient flow and has a closed-form solution in the case of vertex-transitive and path graphs.\nFinally\, if time permits I will draw a connection with the geometry of hyperacute simplices\, following the work of Miroslav Fiedler.\nThis work was done in collaboration with Renaud Lambiotte.\n\n\n12/7/2021\nMatthew Jenssen (University of Birmingham)\nTitle: The singularity probability of random symmetric matrices \nAbstract: Let M_n be drawn uniformly from all n by n symmetric matrices with entries in {-1\,1}. In this talk I’ll consider the following basic question: what is the probability that M_n is singular? I’ll discuss recent joint work with Marcelo Campos\, Marcus Michelen and Julian Sahasrabudhe where we show that this probability is exponentially small. I hope to make the talk accessible to a fairly general audience.\n\n\n12/14/2021\nStefan Glock (ETH Zurich)\nTitle: The longest induced path in a sparse random graph \nAbstract: A long-standing problem in random graph theory has been to determine asymptotically the length of a longest induced path in sparse random graphs. Independent work of Luczak and Suen from the 90s showed the existence of an induced path of roughly half the optimal size\, which seems to be a barrier for certain natural approaches. Recently\, in joint work with Draganic and Krivelevich\, we solved this problem. In the talk\, I will discuss the history of the problem and give an overview of the proof.\n\n\n12/21/2021\n\n\n\n\n01/25/2022\nJacob Bourjaily\nPenn State University\, Department of Physics
URL:https://cmsa.fas.harvard.edu/event/combinatorics-physics-and-probability-seminar/
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220330T093000
DTEND;TZID=America/New_York:20220330T103000
DTSTAMP:20260503T143214
CREATED:20240214T035843Z
LAST-MODIFIED:20240502T150948Z
UID:10002518-1648632600-1648636200@cmsa.fas.harvard.edu
SUMMARY:Edge Modes and Gravity
DESCRIPTION:Speaker: Rob Leigh\, UIUC \nTitle: Edge Modes and Gravity \nAbstract:  In this talk I first review some of the many appearances of localized degrees of freedom — edge modes —  in a variety of physical systems. Edge modes are implicated for example in quantum entanglement and in various topological and holographic dualities. I then review recent work in which it has been realized that a careful treatment of such modes\, paying attention to relevant symmetries\, is required in order to properly understand such basic physical quantities as Noether charges. From many points of view\, it is conjectured that this physics may be pointing at basic properties of quantum spacetimes and gravity.
URL:https://cmsa.fas.harvard.edu/event/edge-modes-and-gravity/
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/02CMSA-Colloquium-03.30.2022-2.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220330T093000
DTEND;TZID=America/New_York:20220330T103000
DTSTAMP:20260503T143214
CREATED:20240214T080954Z
LAST-MODIFIED:20240301T113038Z
UID:10002582-1648632600-1648636200@cmsa.fas.harvard.edu
SUMMARY:Elliptic chiral homology and chiral index
DESCRIPTION:Abstract: We present an effective quantization theory for chiral deformation of two-dimensional conformal field theories. We explain a connection between the quantum master equation and the chiral homology for vertex operator algebras. As an application\, we construct correlation functions of the curved beta-gamma/b-c system and establish a coupled equation relating to chiral homology groups of chiral differential operators. This can be viewed as the vertex algebra analogue of the trace map in algebraic index theory. The talk is based on the recent work arXiv:2112.14572 [math.QA].
URL:https://cmsa.fas.harvard.edu/event/3-29-2022-joint-harvard-cuhk-ymsc-differential-geometry-seminar/
CATEGORIES:Joint Harvard-CUHK-YMSC Differential Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/20220330_Si-LI_poster-1.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220330T103000
DTEND;TZID=America/New_York:20220330T120000
DTSTAMP:20260503T143214
CREATED:20240214T103058Z
LAST-MODIFIED:20240301T064220Z
UID:10002673-1648636200-1648641600@cmsa.fas.harvard.edu
SUMMARY:Renormalization group flow as optimal transport
DESCRIPTION:Youtube Video \n  \nAbstract: We show that Polchinski’s equation for exact renormalization group flow is equivalent to the optimal transport gradient flow of a field-theoretic relative entropy.  This gives a surprising information-theoretic formulation of the exact renormalization group\, expressed in the language of optimal transport.  We will provide reviews of both the exact renormalization group\, as well as the theory of optimal transportation.  Our results allow us to establish a new\, non-perturbative RG monotone\, and also reformulate RG flow as a variational problem.  The latter enables new numerical techniques and allows us to establish a systematic connection between neural network methods and RG flows of conventional field theories.  Our techniques generalize to other RG flow equations beyond Polchinski’s.
URL:https://cmsa.fas.harvard.edu/event/3-30-2022-quantum-matter-in-mathematics-and-physics/
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-03.30.2022-1583x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220330T140000
DTEND;TZID=America/New_York:20220330T150000
DTSTAMP:20260503T143214
CREATED:20230808T183529Z
LAST-MODIFIED:20240515T202223Z
UID:10001209-1648648800-1648652400@cmsa.fas.harvard.edu
SUMMARY:Memorizing Transformers
DESCRIPTION:Speaker: Yuhuai Wu\, Stanford and Google \nTitle: Memorizing Transformers \nAbstract: Language models typically need to be trained or fine-tuned in order to acquire new knowledge\, which involves updating their weights. We instead envision language models that can simply read and memorize new data at inference time\, thus acquiring new knowledge immediately. In this talk\, I will discuss how we extend language models with the ability to memorize the internal representations of past inputs. We demonstrate that an approximate NN lookup into a non-differentiable memory of recent (key\, value) pairs improves language modeling across various benchmarks and tasks\, including generic webtext (C4)\, math papers (arXiv)\, books (PG-19)\, code (Github)\, as well as formal theorems (Isabelle). We show that the performance steadily improves when we increase the size of memory up to 262K tokens. We also find that the model is capable of making use of newly defined functions and theorems during test time.
URL:https://cmsa.fas.harvard.edu/event/3-30-2022-new-technologies-in-mathematics-seminar/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-03.30.2022-1583x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220331T152000
DTEND;TZID=America/New_York:20220331T172000
DTSTAMP:20260503T143214
CREATED:20240214T113726Z
LAST-MODIFIED:20240301T103621Z
UID:10002704-1648740000-1648747200@cmsa.fas.harvard.edu
SUMMARY:Compactification of an embedded vector space and its combinatorics
DESCRIPTION:Abstract: Matroids are combinatorial abstractions of vector spaces embedded in a coordinate space.  Many fundamental questions have been open for these classical objects.  We highlight some recent progress that arise from the interaction between matroid theory and algebraic geometry.  Key objects involve compactifications of embedded vector spaces\, and an exceptional Hirzebruch-Riemann-Roch isomorphism between the K-ring of vector bundles and the cohomology ring of stellahedral varieties.
URL:https://cmsa.fas.harvard.edu/event/3-31-2022-interdisciplinary-science-seminar/
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-03.231.2022-1583x2048-1.jpg
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