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DTSTART;TZID=America/New_York:20210913T090000
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DTSTAMP:20260412T055440
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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:20260412T055440
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:20260412T055440
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:20220301T090000
DTEND;TZID=America/New_York:20220301T100000
DTSTAMP:20260412T055440
CREATED:20240214T045733Z
LAST-MODIFIED:20240304T060140Z
UID:10002534-1646125200-1646128800@cmsa.fas.harvard.edu
SUMMARY:Rational Polypols
DESCRIPTION:Abstract: Eugene Wachspress introduced polypols as real bounded semialgebraic sets in the plane that generalize polygons. He aimed to generalize barycentric coordinates from triangles to arbitrary polygons and further to polypols. For this\, he defined the adjoint curve of a rational polypol. In the study of scattering amplitudes in physics\, positive geometries are real semialgebraic sets together with a rational canonical form. We combine these two worlds by providing an explicit formula for the canonical form of a rational polypol in terms of defining equations of the adjoint curve and the facets of the polypol. For the special case of polygons\, we show that the adjoint curve is hyperbolic and provide an explicit description of its nested ovals. Finally\, we discuss the map that associates the adjoint curve to a given rational polypol\, in particular the cases where this map is finite. For instance\, using monodromy we find that a general quartic curve is the adjoint of 864 heptagons. \nThis talk is based on joint work with R. Piene\, K. Ranestad\, F. Rydell\, B. Shapiro\, R. Sinn\,  M.-S. Sorea\, and S. Telen.
URL:https://cmsa.fas.harvard.edu/event/3-1-2022-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-3.01.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220301T093000
DTEND;TZID=America/New_York:20220301T103000
DTSTAMP:20260412T055440
CREATED:20230825T075625Z
LAST-MODIFIED:20240304T083139Z
UID:10001291-1646127000-1646130600@cmsa.fas.harvard.edu
SUMMARY:Virtual localization for Artin stacks
DESCRIPTION:Abstract: This is a report about work in progress with: Adeel Khan\, Aloysha Latyntsev\, Hyeonjun Park and Charanya Ravi. We will describe a virtual Atiyah-Bott formula for Artin stacks.  In the Deligne-Mumford case our methods allow us to remove the global resolution hypothesis for the virtual normal bundle.
URL:https://cmsa.fas.harvard.edu/event/virtual-localization-for-artin-stacks/
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-02.22.2022-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220301T100000
DTEND;TZID=America/New_York:20220517T130000
DTSTAMP:20260412T055440
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:20220302T093000
DTEND;TZID=America/New_York:20220302T103000
DTSTAMP:20260412T055440
CREATED:20240214T040557Z
LAST-MODIFIED:20240222T171906Z
UID:10002521-1646213400-1646217000@cmsa.fas.harvard.edu
SUMMARY:Dimers and webs
DESCRIPTION:Speaker: Richard Kenyon (Yale) \nTitle: Dimers and webs \nAbstract: We consider SL_n-local systems on graphs on surfaces and show how the associated Kasteleyn matrix can be used to compute probabilities of various topological events involving the overlay of n independent dimer covers (or “n-webs”). \nThis is joint work with Dan Douglas and Haolin Shi.
URL:https://cmsa.fas.harvard.edu/event/dimers-and-webs/
LOCATION:Virtual
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/02CMSA-Colloquium-03.02.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220302T093000
DTEND;TZID=America/New_York:20220302T223000
DTSTAMP:20260412T055440
CREATED:20240214T092842Z
LAST-MODIFIED:20240301T113401Z
UID:10002629-1646213400-1646260200@cmsa.fas.harvard.edu
SUMMARY:Tropical Lagrangian multi-sections and locally free sheaves
DESCRIPTION:Abstract: The SYZ proposal suggests that mirror symmetry is T-duality. It is a folklore that locally free sheaves are mirror to a Lagrangian multi-section of the SYZ fibration. In this talk\, I will introduce the notion of tropical Lagrangian multi-sections and discuss how to obtain from such object to a class of locally free sheaves on the log Calabi-Yau spaces that Gross-Siebert have considered. I will also discuss a joint work with Kwokwai Chan and Ziming Ma\, where we proved the smoothability of a class of locally free sheaves on some log Calabi-Yau surfaces by using combinatorial data obtained from tropical Lagrangian multi-sections.
URL:https://cmsa.fas.harvard.edu/event/3-1-2022-joint-harvard-cuhk-ymsc-differential-geometry-seminar/
CATEGORIES:Joint Harvard-CUHK-YMSC Differential Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/20220302_Yat-Hin-SUEN_poster-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220302T103000
DTEND;TZID=America/New_York:20220302T120000
DTSTAMP:20260412T055440
CREATED:20240214T105827Z
LAST-MODIFIED:20240301T070805Z
UID:10002688-1646217000-1646222400@cmsa.fas.harvard.edu
SUMMARY:Exactly Solvable Lattice Hamiltonians and Gravitational Anomalies
DESCRIPTION:Abstract: We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions\, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase “w2w3” in (4+1)D that has an anomalous boundary topological order with fermionic particle and fermionic loop excitations that have mutual statistics. Finally\, we will demonstrate a few examples of fermionic loop excitations.
URL:https://cmsa.fas.harvard.edu/event/3-2-2022-quantum-matter-in-mathematics-and-physics/
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-03.02.2022-1544x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220302T140000
DTEND;TZID=America/New_York:20220302T150000
DTSTAMP:20260412T055440
CREATED:20230808T182233Z
LAST-MODIFIED:20240517T193649Z
UID:10001206-1646229600-1646233200@cmsa.fas.harvard.edu
SUMMARY:Scaling Laws and Their Implications for Coding AI
DESCRIPTION:Speaker: Jared Kaplan\, Johns Hopkins Dept. of Physics & Astronomy \nTitle: Scaling Laws and Their Implications for Coding AI \nAbstract:  Scaling laws and associated downstream trends can be used as an organizing principle when thinking about current and future ML progress.  I will briefly review scaling laws for generative models in a number of domains\, emphasizing language modeling.  Then I will discuss scaling results for transfer from natural language to code\, and results on python programming performance from “codex” and other models.  If there’s time I’ll discuss prospects for the future — limitations from dataset sizes\, and prospects for RL and other techniques.
URL:https://cmsa.fas.harvard.edu/event/3-2-2022-new-technologies-in-mathematics-seminar/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/03.2.2022-1553x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220303T093000
DTEND;TZID=America/New_York:20220303T110000
DTSTAMP:20260412T055440
CREATED:20240214T105412Z
LAST-MODIFIED:20240813T163614Z
UID:10002684-1646299800-1646305200@cmsa.fas.harvard.edu
SUMMARY:Callan Rubakov Effect and Higher Charge Monopoles
DESCRIPTION:Abstract: In this talk we will discuss the interaction between magnetic monopoles and massless fermions. In the 1980’s Callan and Rubakov showed that in the simplest example and that fermion-monopole interactions catalyze proton decay in GUT completions of the standard model. Here we will explain how fermions in general representations interact with general spherically symmetric monopoles and classify the types of symmetries that are broken: global symmetries with ABJ-type anomalies.
URL:https://cmsa.fas.harvard.edu/event/3-3-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-03.03.2022-1544x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220303T151100
DTEND;TZID=America/New_York:20220303T161100
DTSTAMP:20260412T055440
CREATED:20240215T091737Z
LAST-MODIFIED:20240301T104734Z
UID:10002711-1646320260-1646323860@cmsa.fas.harvard.edu
SUMMARY:Towards Understanding Training Dynamics for Mildly Overparametrized Models
DESCRIPTION:Abstract: While over-parameterization is widely believed to be crucial for the success of optimization for the neural networks\, most existing theories on over-parameterization do not fully explain the reason — they either work in the Neural Tangent Kernel regime where neurons don’t move much\, or require an enormous number of neurons. In this talk I will describe our recent works towards understanding training dynamics that go beyond kernel regimes with only polynomially many neurons (mildly overparametrized). In particular\, we first give a local convergence result for mildly overparametrized two-layer networks. We then analyze the global training dynamics for a related overparametrized tensor model. For both works\, we rely on a key intuition that neurons in overparametrized models work in groups and it’s important to understand the behavior of an average neuron in the group. Based on two works: https://arxiv.org/abs/2102.02410 and https://arxiv.org/abs/2106.06573. \nBio: Professor Rong Ge is Associate Professor of Computer Science at Duke University. He received his Ph.D. from the Computer Science Department of Princeton University\, supervised by Sanjeev Arora. He was a post-doc at Microsoft Research\, New England. In 2019\, he received both a Faculty Early Career Development Award from the National Science Foundation and the prestigious Sloan Research Fellowship. His research interest focus on theoretical computer science and machine learning. Modern machine learning algorithms such as deep learning try to automatically learn useful hidden representations of the data. He is interested in formalizing hidden structures in the data and designing efficient algorithms to find them. His research aims to answer these questions by studying problems that arise in analyzing text\, images\, and other forms of data\, using techniques such as non-convex optimization and tensor decompositions.
URL:https://cmsa.fas.harvard.edu/event/3-3-2022-interdisciplinary-science-seminar/
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-03.03.2022-1583x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220304T093000
DTEND;TZID=America/New_York:20220304T103000
DTSTAMP:20260412T055440
CREATED:20240214T085309Z
LAST-MODIFIED:20240301T111217Z
UID:10002600-1646386200-1646389800@cmsa.fas.harvard.edu
SUMMARY:Positive Mass\, Density\, and Scalar Curvature on Noncompact Manifolds
DESCRIPTION:Member Seminar \nSpeaker: Martin Lesourd \nTitle: Positive Mass\, Density\, and Scalar Curvature on Noncompact Manifolds \nAbstract: I’ll describe some recent work spanning a couple of different papers on the topics mentioned in the title: Positive Mass\, Density\, and Scalar Curvature on Noncompact Manifolds. Two of these are with R. Unger\, Prof. S-T. Yau\, and two others are with R. Unger\, and Prof. D. A. Lee.
URL:https://cmsa.fas.harvard.edu/event/3-4-2022-member-seminar/
LOCATION:Hybrid – G10
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220307T100000
DTEND;TZID=America/New_York:20220307T113000
DTSTAMP:20260412T055440
CREATED:20230730T175629Z
LAST-MODIFIED:20240301T073931Z
UID:10001144-1646647200-1646652600@cmsa.fas.harvard.edu
SUMMARY:4d strings at strong coupling
DESCRIPTION:Speakers: Fernando Marchesano (UAM-CSIC\, Madrid)  and Max Wiesner (Harvard CMSA)\n\n\n\nTitle: 4d strings at strong coupling\n\n\nAs usual\, the format will be 45 min talk + 30 min discussion\, to encourage participation from the audience.\nLooking forward to seeing you there!
URL:https://cmsa.fas.harvard.edu/event/3-7-2022-swampland-seminar/
LOCATION:Virtual
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220308T090000
DTEND;TZID=America/New_York:20220308T100000
DTSTAMP:20260412T055440
CREATED:20240214T064241Z
LAST-MODIFIED:20240304T090552Z
UID:10002550-1646730000-1646733600@cmsa.fas.harvard.edu
SUMMARY:Greedy maximal independent sets via local limits
DESCRIPTION:Abstract: The random greedy algorithm for finding a maximal independent set in a graph has been studied extensively in various settings in combinatorics\, probability\, computer science\, and chemistry. The algorithm builds a maximal independent set by inspecting the graph’s vertices one at a time according to a random order\, adding the current vertex to the independent set if it is not connected to any previously added vertex by an edge. \nIn this talk\, I will present a simple yet general framework for calculating the asymptotics of the proportion of the yielded independent set for sequences of (possibly random) graphs\, involving a valuable notion of local convergence. I will demonstrate the applicability of this framework by giving short and straightforward proofs for results on previously studied families of graphs\, such as paths and various random graphs\, and by providing new results for other models such as random trees. \nIf time allows\, I will discuss a more delicate (and combinatorial) result\, according to which\, in expectation\, the cardinality of a random greedy independent set in the path is no larger than that in any other tree of the same order. \nThe talk is based on joint work with Michael Krivelevich\, Tamás Mészáros and Clara Shikhelman.
URL:https://cmsa.fas.harvard.edu/event/3-8-2022-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-3.08.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220309T093000
DTEND;TZID=America/New_York:20220309T103000
DTSTAMP:20260412T055440
CREATED:20240214T040341Z
LAST-MODIFIED:20240304T074318Z
UID:10002520-1646818200-1646821800@cmsa.fas.harvard.edu
SUMMARY:Side-effects of Learning from Low Dimensional Data Embedded in an Euclidean Space
DESCRIPTION:Abstract: The  low  dimensional  manifold  hypothesis  posits  that  the  data  found  in many applications\, such as those involving natural images\, lie (approximately) on low dimensional manifolds embedded in a high dimensional Euclidean space. In this setting\, a typical neural network defines a function that takes a finite number of vectors in the embedding space as input.  However\, one often needs to  consider  evaluating  the  optimized  network  at  points  outside  the  training distribution.  We analyze the cases where the training data are distributed in a linear subspace of Rd.  We derive estimates on the variation of the learning function\, defined by a neural network\, in the direction transversal to the subspace.  We study the potential regularization effects associated with the network’s depth and noise in the codimension of the data manifold.
URL:https://cmsa.fas.harvard.edu/event/side-effects-of-learning-from-low-dimensional-data-embedded-in-an-euclidean-space/
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/02CMSA-Colloquium-03.09.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220309T103000
DTEND;TZID=America/New_York:20220309T120000
DTSTAMP:20260412T055440
CREATED:20240214T105142Z
LAST-MODIFIED:20240301T070302Z
UID:10002682-1646821800-1646827200@cmsa.fas.harvard.edu
SUMMARY:Anomalies\, topological insulators and Kaehler-Dirac fermions
DESCRIPTION:Abstract: Motivated by a puzzle arising from recent work on staggered lattice fermions we introduce Kaehler-Dirac fermions and describe their connection both to Dirac fermions and staggered fermions. We show that they suffer from a gravitational anomaly that breaks a chiral U(1) symmetry specific to Kaehler-Dirac fermions down to Z_4 in any even dimension. In odd dimensions we show that the effective theory that results from integrating out massive Kaehler-Dirac fermions is a topological gravity theory. Such theories generalize Witten’s construction of (2+1) gravity as a Chern Simons theory. In the presence of a domain wall massless modes appear on the wall which can be consistently coupled to gravity due to anomaly inflow from the bulk gravitational theory. Much of this story parallels the usual discussion of topological insulators. The key difference is that the twisted chiral symmetry and anomaly structure of Kaehler-Dirac theories survives intact under discretization and governs the behavior of the lattice models. $Z_4$ invariant four fermion interactions can be used to gap out states in such theories without breaking symmetries and in flat space yields the known constraints on the number of Majorana fermions needed symmetric mass generation namely eight and sixteen Majorana spinors in two and four dimensions.
URL:https://cmsa.fas.harvard.edu/event/3-9-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-03.09.2022-1544x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220309T140000
DTEND;TZID=America/New_York:20220309T140000
DTSTAMP:20260412T055440
CREATED:20230808T182829Z
LAST-MODIFIED:20240813T160025Z
UID:10001207-1646834400-1646834400@cmsa.fas.harvard.edu
SUMMARY:Machine Learning 30 STEM Courses in 12 Departments
DESCRIPTION:Speaker: Iddo Drori\, MIT EE&CS and Columbia School of Engineering \nTitle: Machine Learning 30 STEM Courses in 12 Departments \nAbstract: We automatically solve\, explain\, and generate university-level course problems from thirty STEM courses (at MIT\, Harvard\, and Columbia) for the first time.\nWe curate a new dataset of course questions and answers across a dozen departments: Aeronautics and Astronautics\, Chemical Engineering\, Chemistry\, Computer Science\, Economics\, Electrical Engineering\, Materials Science\, Mathematics\, Mechanical Engineering\, Nuclear Science\, Physics\, and Statistics.\nWe generate new questions and use them in a Columbia University course\, and perform A/B tests demonstrating that these machine generated questions are indistinguishable from human-written questions and that machine generated explanations are as useful as human-written explanations\, again for the first time.\nOur approach consists of five steps:\n(i) Given course questions\, turn them into programming tasks;\n(ii) Automatically generate programs from the programming tasks using a Transformer model\, OpenAI Codex\, pre-trained on text and fine-tuned on code;\n(iii) Execute the programs to obtain and evaluate the answers;\n(iv) Automatically explain the correct solutions using Codex;\n(v) Automatically generate new questions that are qualitatively indistinguishable from human-written questions.\nThis work is a significant step forward in applying machine learning for education\, automating a considerable part of the work involved in teaching.\nOur approach allows personalization of questions based on difficulty level and student backgrounds\, and scales up to a broad range of courses across the schools of engineering and science. \nThis is joint work with students and colleagues at MIT\, Harvard University\, Columbia University\, Worcester Polytechnic Institute\, and the University of Waterloo.
URL:https://cmsa.fas.harvard.edu/event/3-9-2022-new-technologies-in-mathematics-seminar/
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-03.09.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220310T130000
DTEND;TZID=America/New_York:20220310T140000
DTSTAMP:20260412T055440
CREATED:20240214T080539Z
LAST-MODIFIED:20240813T160832Z
UID:10002579-1646917200-1646920800@cmsa.fas.harvard.edu
SUMMARY:The Einstein-flow on manifolds of negative curvature
DESCRIPTION:Abstract: We consider the Cauchy problem for the Einstein equations for cosmological spacetimes\, i.e. spacetimes with compact spatial hypersurfaces. Various classes of those dynamical spacetimes have been constructed and analyzed using CMC foliations or equivalently the CMC-Einstein flow. We will briefly review the Andersson-Moncrief stability result of negative Einstein metrics under the vacuum Einstein flow and then present various recent generalizations to the nonvacuum case. We will emphasize what difficulties arise in those generalizations\, how they can be handled depending on the matter model at hand\, and what implications we can draw from these results for cosmology. We then turn to a scenario where the CMC Einstein flow leads to a large data result in 2+1-dimensions.
URL:https://cmsa.fas.harvard.edu/event/3-10-2022-general-relativity-seminar/
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-03.10.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220310T151300
DTEND;TZID=America/New_York:20220310T161300
DTSTAMP:20260412T055440
CREATED:20240215T091511Z
LAST-MODIFIED:20240301T104543Z
UID:10002710-1646925180-1646928780@cmsa.fas.harvard.edu
SUMMARY:Virtual Teams in Gig Economy — An End-to-End Data Science Approach
DESCRIPTION:Abstract: The gig economy provides workers with the benefits of autonomy and flexibility\, but it does so at the expense of work identity and co-worker bonds. Among the many reasons why gig workers leave their platforms\, an unexplored aspect is the organization identity. In a series of studies\, we develop a team formation and inter-team contest at a ride-sharing platform. We employ an end-to-end data science approach\, combining methodologies from randomized field experiments\, recommender systems\, and counterfactual machine learning. Together\, our results show that platform designers can leverage team identity and team contests to increase revenue and worker engagement in a gig economy. \nBio: Wei Ai is an Assistant Professor in the College of Information Studies (iSchool) and the Institute for Advanced Computer Studies (UMIACS) at the University of Maryland. His research interest lies in data science for social good\, where the advances of machine learning and data analysis algorithms translate into measurable impacts on society. He combines machine learning\, causal inference\, and field experiments in his research\, and has rich experience in collaborating with industrial partners. He earned his Ph.D. from the School of Information at the University of Michigan. His research has been published in top journals and conferences\, including PNAS\, ACM TOIS\, WWW\, and ICWSM.
URL:https://cmsa.fas.harvard.edu/event/3-10-2022-interdisciplinary-science-seminar/
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-03.10.2022-1583x2048-1-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220310T200000
DTEND;TZID=America/New_York:20220310T213000
DTSTAMP:20260412T055440
CREATED:20240214T104900Z
LAST-MODIFIED:20240813T163724Z
UID:10002680-1646942400-1646947800@cmsa.fas.harvard.edu
SUMMARY:Resonant side-jump thermal Hall effect of phonons coupled to dynamical defects
DESCRIPTION:Abstract: We present computations of the thermal Hall coefficient of phonons scattering off defects with multiple energy levels. Using a microscopic formulation based on the Kubo formula\, we find that the leading contribution perturbative in the phonon-defect coupling is of the ‘side-jump’ type\, which is proportional to the phonon lifetime. This contribution is at resonance when the phonon energy equals a defect level spacing. Our results are obtained for different defect models\, and include models of an impurity quantum spin in the presence of quasi-static magnetic order with an isotropic Zeeman coupling to the applied field. \nThis work is based on arxiv: 2201.11681
URL:https://cmsa.fas.harvard.edu/event/3-10-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-03.10.2022-1544x2048-1-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220315T090000
DTEND;TZID=America/New_York:20220315T100000
DTSTAMP:20260412T055440
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:20260412T055440
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:20260412T055440
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:20260412T055440
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:20260412T055440
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:20260412T055440
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:20260412T055440
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:20260412T055440
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:20260412T055440
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
END:VCALENDAR