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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220215T093000
DTEND;TZID=America/New_York:20220215T103000
DTSTAMP:20260516T065125
CREATED:20230818T054001Z
LAST-MODIFIED:20240304T083319Z
UID:10001289-1644917400-1644921000@cmsa.fas.harvard.edu
SUMMARY:Virtual Coulomb branch and quantum K-theory
DESCRIPTION:Abstract: In this talk\, I will introduce a virtual variant of the quantized Coulomb branch constructed by Braverman-Finkelberg-Nakajima\, where the convolution product is modified by a virtual intersection. The resulting virtual Coulomb branch acts on the moduli space of quasimaps into the holomorphic symplectic quotient T^*N//G. When G is abelian\, over the torus fixed points\, this representation is a Verma module. The vertex function\, a K-theoretic enumerative invariant introduced by A. Okounkov\, can be expressed as a Whittaker function of the algebra. The construction also provides a description of the quantum q-difference module. As an application\, this gives a proof of the invariance of the quantum q-difference module under variation of GIT.
URL:https://cmsa.fas.harvard.edu/event/virtual-coulomb-branch-and-quantum-k-theory/
LOCATION:Virtual
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220215T090000
DTEND;TZID=America/New_York:20220215T100000
DTSTAMP:20260516T065125
CREATED:20240213T104814Z
LAST-MODIFIED:20240304T100739Z
UID:10002456-1644915600-1644919200@cmsa.fas.harvard.edu
SUMMARY:Equiangular lines and regular graphs
DESCRIPTION:Abstract: 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.
URL:https://cmsa.fas.harvard.edu/event/2-15-2022-combinatorics-physics-and-probability-seminar/
CATEGORIES:Combinatorics Physics and Probability
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220211T093000
DTEND;TZID=America/New_York:20220211T103000
DTSTAMP:20260516T065125
CREATED:20240214T085713Z
LAST-MODIFIED:20240301T111928Z
UID:10002602-1644571800-1644575400@cmsa.fas.harvard.edu
SUMMARY:Amplituhedra\, Scattering Amplitudes and Triangulations
DESCRIPTION:Member Seminar \nSpeaker: Matteo Parisi \nTitle: Amplituhedra\, Scattering Amplitudes and Triangulations \nAbstract: In this talk I will discuss about Amplituhedra – generalizations of polytopes inside the Grassmannian – recently introduced by physicists as new geometric constructions encoding interactions of elementary particles in certain Quantum Field Theories. In particular\, I will explain how the problem of finding triangulations of Amplituhedra is connected to computing scattering amplitudes of N=4 super Yang-Mills theory. Triangulations of polygons are encoded in the associahedron studied by Stasheff in the sixties; in the case of polytopes\, triangulations are captured by secondary polytopes constructed by Gelfand et al. in the nineties. Whereas a “secondary” geometry describing triangulations of Amplituhedra is still not known\, and we pave the way for such studies. We will discuss how the combinatorics of triangulations interplays with T-duality from String Theory\, in connection with a dual object we define – the Momentum Amplituhedron. A generalization of T-duality led us to discover a striking duality between triangulations of Amplituhedra of “m=2” type and the ones of a seemingly unrelated object – the Hypersimplex. The latter is a polytope which has been central in many contexts\, such as matroid theory\, torus orbits in the Grassmannian\, and tropical geometry. Based on joint works with Lauren Williams\, Melissa Sherman-Bennett\, Tomasz Lukowski [arXiv:2104.08254\, arXiv:2002.06164].
URL:https://cmsa.fas.harvard.edu/event/2-11-2022-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220210T150000
DTEND;TZID=America/New_York:20220210T160000
DTSTAMP:20260516T065125
CREATED:20240215T092349Z
LAST-MODIFIED:20240301T105720Z
UID:10002716-1644505200-1644508800@cmsa.fas.harvard.edu
SUMMARY:2/10/2022 – Interdisciplinary Science Seminar
DESCRIPTION:Title: Metric Algebraic Geometry \nAbstract: A real algebraic variety is the set of points in real Euclidean space that satisfy a system of polynomial equations. Metric algebraic geometry is the study of properties of real algebraic varieties that depend on a distance metric. In this talk\, we introduce metric algebraic geometry through a discussion of Voronoi cells\, bottlenecks\, and the reach of an algebraic variety. We also show applications to the computational study of the geometry of data with nonlinear models.
URL:https://cmsa.fas.harvard.edu/event/2-10-2022-interdisciplinary-science-seminar/
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-2.10.2022-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220210T130000
DTEND;TZID=America/New_York:20220210T143000
DTSTAMP:20260516T065125
CREATED:20230824T172419Z
LAST-MODIFIED:20240304T083923Z
UID:10001307-1644498000-1644503400@cmsa.fas.harvard.edu
SUMMARY:Active Matter Controlling Epithelial Dynamics
DESCRIPTION:Abstract: My lab is interested in the active and adaptive materials that underlie control of cell shape.  This has centered around understanding force transmission and sensing within the actin cytoskeleton.  I will first review our current understanding of the types of active matter that can be constructed by actin polymers.  I will then turn to our recent experiments to understand how Cell shape changes in epithelial tissue.  I will describe the two sources of active stresses within these tissues\, one driven by the cell cycle and controlling cell-cell stresses and the other controlled by cell-matrix signaling controlling motility.  I will then briefly describe how we are using optogenetics to locally control active stresses to reveal adaptive and force-sensitive mechanics of the cytoskeletal machinery. Hopefully\, I will convince you that recent experimental and theoretical advances make this a very promising time to study this quite complicated form of active matter.
URL:https://cmsa.fas.harvard.edu/event/active-matter-controlling-epithelial-dynamics/
CATEGORIES:Active Matter Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Active-Matter-Seminar-02.10.22-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220210T093000
DTEND;TZID=America/New_York:20220210T110000
DTSTAMP:20260516T065125
CREATED:20240214T100805Z
LAST-MODIFIED:20240301T072127Z
UID:10002658-1644485400-1644490800@cmsa.fas.harvard.edu
SUMMARY:The global structure of the Standard Model and new nonperturbative processes
DESCRIPTION:Speaker: Mohamed Anber (Durham University) \nTitle: The global structure of the Standard Model and new nonperturbative processes \nAbstract: It is well-established that the Standard Model (SM) of particle physics is based on su(3)Xsu(2)Xu(1) Lie-algebra. What is less appreciated\, however\, is that SM accommodates a Z_6 1-form global symmetry.  Gauging this symmetry\, or a subgroup of it\, changes the global structure of the SM gauge group and amounts to summing over sectors of instantons with fractional topological charges. After a brief review of the concept of higher-form symmetries\, I will explain the origin of the Z_6 1-form symmetry and construct the explicit fractional-instanton solutions on compact manifolds. The new instantons mediate baryon-number and lepton-number violating processes\, which can win over the weak BPST-instanton processes\, provided that SM accommodates extra hyper-charged particles above the TeV scale. I will also comment on the cosmological aspects of the new solutions.
URL:https://cmsa.fas.harvard.edu/event/2-10-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-02.10.2022-1544x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220210T093000
DTEND;TZID=America/New_York:20220210T103000
DTSTAMP:20260516T065125
CREATED:20240304T103339Z
LAST-MODIFIED:20240304T103339Z
UID:10002899-1644485400-1644489000@cmsa.fas.harvard.edu
SUMMARY:Dihedral ridigity and mass
DESCRIPTION:Abstract: To characterise scalar curvature\, Gromov proposed the dihedral rigidity conjecture which states that a positively curved polyhedron having dihedral angles less than those of a corresponding flat polyhedron should be isometric to a flat one. In this talk\, we will discuss some recent progress on this conjecture and its connection with general relativity (ADM mass and quasilocal mass).
URL:https://cmsa.fas.harvard.edu/event/2-10-2022-general-relativity-seminar/
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220209T200000
DTEND;TZID=America/New_York:20220209T213000
DTSTAMP:20260516T065125
CREATED:20240214T103129Z
LAST-MODIFIED:20240301T072509Z
UID:10002674-1644436800-1644442200@cmsa.fas.harvard.edu
SUMMARY:On the absence of global anomalies of heterotic string theories
DESCRIPTION:Speaker: Yuji Tachikawa (Kavli IPMU\, U Tokyo) \nTitle: On the absence of global anomalies of heterotic string theories \nAbstract: Superstring theory as we know it started from the discovery by Green and Schwarz in 1984 that the perturbative anomalies of heterotic strings miraculously cancel. But the cancellation of global anomalies of heterotic strings remained an open problem for a long time. \nIn this talk\, I would like to report how this issue was finally resolved last year\, by combining two developments outside of string theory. Namely\, on one hand\, the study of topological phases in condensed matter theory has led to our vastly improved understanding of the general form of global anomalies. On the other hand\, the study of topological modular forms in algebraic topology allows us to constrain the data of heterotic worldsheet theories greatly\, as far as their contributions to the anomalies are concerned. Putting them together\, it is possible to show that global anomalies of heterotic strings are always absent. \nThe talk is based on https://arxiv.org/abs/2103.12211 and https://arxiv.org/abs/2108.13542 \, in collaboration with Mayuko Yamashita.
URL:https://cmsa.fas.harvard.edu/event/2-9-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-02.09.2022-1544x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220209T140000
DTEND;TZID=America/New_York:20220209T150000
DTSTAMP:20260516T065125
CREATED:20230808T181534Z
LAST-MODIFIED:20240517T193404Z
UID:10001204-1644415200-1644418800@cmsa.fas.harvard.edu
SUMMARY:Toward Demystifying Transformers and Attention
DESCRIPTION:Speaker: Ben Edelman\, Harvard Computer Science \nTitle: Toward Demystifying Transformers and Attention \nAbstract: Over the past several years\, attention mechanisms (primarily in the form of the Transformer architecture) have revolutionized deep learning\, leading to advances in natural language processing\, computer vision\, code synthesis\, protein structure prediction\, and beyond. Attention has a remarkable ability to enable the learning of long-range dependencies in diverse modalities of data. And yet\, there is at present limited principled understanding of the reasons for its success. In this talk\, I’ll explain how attention mechanisms and Transformers work\, and then I’ll share the results of a preliminary investigation into why they work so well. In particular\, I’ll discuss an inductive bias of attention that we call sparse variable creation: bounded-norm Transformer layers are capable of representing sparse Boolean functions\, with statistical generalization guarantees akin to sparse regression.
URL:https://cmsa.fas.harvard.edu/event/2-9-2022-new-technologies-in-mathematics-seminar/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-02.09.2022-1553x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220209T090000
DTEND;TZID=America/New_York:20220209T220000
DTSTAMP:20260516T065125
CREATED:20240201T022446Z
LAST-MODIFIED:20240202T154640Z
UID:10001526-1644397200-1644444000@cmsa.fas.harvard.edu
SUMMARY:Geodesics and minimal surfaces
DESCRIPTION:Abstract: There are several properties of closed geodesics which are proven using its Hamiltonian formulation\, which has no analogue for minimal surfaces. I will talk about some recent progress in proving some of these properties for minimal surfaces.
URL:https://cmsa.fas.harvard.edu/event/2-8-2022-joint-harvard-cuhk-ymsc-differential-geometry-seminar/
CATEGORIES:Joint Harvard-CUHK-YMSC Differential Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/20220209_Andre-Neves_poster.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220208T213000
DTEND;TZID=America/New_York:20220208T223000
DTSTAMP:20260516T065125
CREATED:20240214T041520Z
LAST-MODIFIED:20240501T205116Z
UID:10002524-1644355800-1644359400@cmsa.fas.harvard.edu
SUMMARY:Tetrahedron instantons and M-theory indices
DESCRIPTION:Colloquium \nSpeaker: Wenbin Yan (Tsinghua University) \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.
URL:https://cmsa.fas.harvard.edu/event/tetrahedron-instantons-and-m-theory-indices/
LOCATION:Virtual
CATEGORIES:Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220208T093000
DTEND;TZID=America/New_York:20220208T223000
DTSTAMP:20260516T065125
CREATED:20240304T103644Z
LAST-MODIFIED:20240304T103644Z
UID:10002900-1644312600-1644359400@cmsa.fas.harvard.edu
SUMMARY:CMSA Colloquium
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\n\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-10/
CATEGORIES:Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220208T093000
DTEND;TZID=America/New_York:20220208T103000
DTSTAMP:20260516T065125
CREATED:20230818T051427Z
LAST-MODIFIED:20240304T083416Z
UID:10001287-1644312600-1644316200@cmsa.fas.harvard.edu
SUMMARY:SYZ Conjecture beyond Mirror Symmetry
DESCRIPTION:Abstract: Strominger-Yau-Zaslow conjecture is one of the guiding principles in mirror symmetry\, which not only predicts the geometric structures of Calabi-Yau manifolds but also provides a recipe for mirror construction. Besides mirror symmetry\, the SYZ conjecture itself is the holy grail in geometrical analysis and closely related to the behavior of the Ricci-flat metrics. In this talk\, we will explain how SYZ fibrations on log Calabi-Yau surfaces detect the non-standard semi-flat metric which generalized the semi-flat metrics of Greene-Shapere-Vafa-Yau. Furthermore\, we will use the SYZ fibration on log Calabi-Yau surfaces to prove the Torelli theorem of gravitational instantons of type ALH^*. This is based on the joint works with T. Collins and A. Jacob.
URL:https://cmsa.fas.harvard.edu/event/syz-conjecture-beyond-mirror-symmetry/
LOCATION:Virtual
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220208T090000
DTEND;TZID=America/New_York:20220208T100000
DTSTAMP:20260516T065125
CREATED:20240213T104820Z
LAST-MODIFIED:20240304T105941Z
UID:10002457-1644310800-1644314400@cmsa.fas.harvard.edu
SUMMARY:Invariant theory for maximum likelihood estimation
DESCRIPTION:Abstract:  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.
URL:https://cmsa.fas.harvard.edu/event/2-8-2022-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-2.8.2022-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220207T130000
DTEND;TZID=America/New_York:20220207T140000
DTSTAMP:20260516T065125
CREATED:20240214T110354Z
LAST-MODIFIED:20240301T074524Z
UID:10002690-1644238800-1644242400@cmsa.fas.harvard.edu
SUMMARY:Holomorphic CFTs and topological modular forms
DESCRIPTION:Abstract: The theory of topological modular forms leads to many interesting constraints and predictions for two-dimensional quantum field theories\, and some of them might have interesting implications for the swampland program. In this talk\, I will show that a conjecture by Segal\, Stolz and Teichner requires the constant term of the partition function of a bosonic holomorphic CFTs to be divisible by specific integers determined by the central charge. We verify this constraint in large classes of physical examples\, and rule out the existence of an infinite set of “extremal CFTs”\, including those with central charges c = 48\, 72\, 96 and 120.
URL:https://cmsa.fas.harvard.edu/event/2-7-2022-swampland-seminar/
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220204T093000
DTEND;TZID=America/New_York:20220204T103000
DTSTAMP:20260516T065125
CREATED:20240214T090103Z
LAST-MODIFIED:20240301T112029Z
UID:10002603-1643967000-1643970600@cmsa.fas.harvard.edu
SUMMARY:Survey on stability of the positive mass theorem
DESCRIPTION:Member Seminar \nSpeaker: Dan Lee \nTitle: Survey on stability of the positive mass theorem \nAbstract: The Riemannian positive mass theorem states that a complete asymptotically flat manifold with nonnegative scalar curvature must have nonnegative ADM mass. This inequality comes with a rigidity statement that says that if the mass is zero\, then the manifold must be Euclidean space. This naturally leads to the question of stability. In this talk\, I will discuss various results related to this question.
URL:https://cmsa.fas.harvard.edu/event/2-4-2022-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220203T145700
DTEND;TZID=America/New_York:20220203T165700
DTSTAMP:20260516T065125
CREATED:20240215T092602Z
LAST-MODIFIED:20240301T105825Z
UID:10002717-1643900220-1643907420@cmsa.fas.harvard.edu
SUMMARY:2/3/2022 – Interdisciplinary Science Seminar
DESCRIPTION:Title:Quasiperiodic prints from triply periodic blocks \nAbstract: Slice a triply periodic wooden sculpture along an irrational plane. If you ink the cut surface and press it against a page\, the pattern you print will be quasiperiodic. Patterns like these help physicists see how metals conduct electricity in strong magnetic fields. I’ll show you some block prints that imitate the printing process described above\, and I’ll point out the visual features that reveal conductivity properties. \nInteractive slides:https://www.ihes.fr/~fenyes/seeing/slices/
URL:https://cmsa.fas.harvard.edu/event/2-3-2022-interdisciplinary-science-seminar/
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-2.03.2022-1583x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220203T113000
DTEND;TZID=America/New_York:20220203T130000
DTSTAMP:20260516T065125
CREATED:20240301T073438Z
LAST-MODIFIED:20240301T073438Z
UID:10002886-1643887800-1643893200@cmsa.fas.harvard.edu
SUMMARY:Quantum Oscillations of Electrical Resistivity in an Insulator
DESCRIPTION:Speaker: Lu Li (U Michigan) \nTitle: Quantum Oscillations of Electrical Resistivity in an Insulator \nAbstract: In metals\, orbital motions of conduction electrons are quantized in magnetic fields\, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators\, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12\, despite much larger than that of usual metals\, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.
URL:https://cmsa.fas.harvard.edu/event/2-3-2022-quantum-matter-in-mathematics-and-physics-2/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220203T113000
DTEND;TZID=America/New_York:20220203T130000
DTSTAMP:20260516T065125
CREATED:20240213T110846Z
LAST-MODIFIED:20240301T073107Z
UID:10002477-1643887800-1643893200@cmsa.fas.harvard.edu
SUMMARY:Quantum Oscillations of Electrical Resistivity in an Insulator
DESCRIPTION:Abstract: In metals\, orbital motions of conduction electrons are quantized in magnetic fields\, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators\, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12\, despite much larger than that of usual metals\, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.
URL:https://cmsa.fas.harvard.edu/event/2-3-2022-quantum-matter-in-mathematics-and-physics/
CATEGORIES:Strongly Correlated Quantum Materials and High-Temperature Superconductors
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-02.03.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220203T090000
DTEND;TZID=America/New_York:20220203T100000
DTSTAMP:20260516T065125
CREATED:20240304T105610Z
LAST-MODIFIED:20240304T105610Z
UID:10002902-1643878800-1643882400@cmsa.fas.harvard.edu
SUMMARY:The Amplituhedron BCFW Triangulation
DESCRIPTION:Abstract:  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.
URL:https://cmsa.fas.harvard.edu/event/2-3-2022-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-2.3.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220202T200000
DTEND;TZID=America/New_York:20220202T213000
DTSTAMP:20260516T065125
CREATED:20240214T110015Z
LAST-MODIFIED:20240301T074259Z
UID:10002687-1643832000-1643837400@cmsa.fas.harvard.edu
SUMMARY:Kramers-Wannier-like duality defects in higher dimensions
DESCRIPTION:Title: Kramers-Wannier-like duality defects in higher dimensions \nAbstract: I will introduce a class of non-invertible topological defects in (3 + 1)d gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1 + 1)d critical Ising model. As in the lower-dimensional case\, the presence of such non-invertible defects implies self-duality under a particular gauging of their discrete (higher-form) symmetries. Examples of theories with such a defect include SO(3) Yang-Mills (YM) at θ = π\, N = 1 SO(3) super YM\, and N = 4 SU(2) super YM at τ = i. I will also explain an analogous construction in (2+1)d\, and give a number of examples in Chern-Simons-matter theories. This talk is based on https://arxiv.org/abs/2111.01141.
URL:https://cmsa.fas.harvard.edu/event/2-2-2022-quantum-matter-in-mathematics-and-physics/
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-02.02.2022-1544x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220202T140000
DTEND;TZID=America/New_York:20220202T150000
DTSTAMP:20260516T065125
CREATED:20230808T181044Z
LAST-MODIFIED:20240515T204958Z
UID:10000006-1643810400-1643814000@cmsa.fas.harvard.edu
SUMMARY:Neural diffusion PDEs\, differential geometry\, and graph neural networks
DESCRIPTION:Speaker: Michael Bronstein\, University of Oxford and Twitter \nTitle: Neural diffusion PDEs\, differential geometry\, and graph neural networks \nAbstract: In this talk\, I will make connections between Graph Neural Networks (GNNs) and non-Euclidean diffusion equations. I will show that drawing on methods from the domain of differential geometry\, it is possible to provide a principled view on such GNN architectural choices as positional encoding and graph rewiring as well as explain and remedy the phenomena of oversquashing and bottlenecks.
URL:https://cmsa.fas.harvard.edu/event/2-2-2022-new-technologies-in-mathematics/
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-02.02.2022-2-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220202T093000
DTEND;TZID=America/New_York:20220202T103000
DTSTAMP:20260516T065125
CREATED:20240214T041742Z
LAST-MODIFIED:20240304T075005Z
UID:10002525-1643794200-1643797800@cmsa.fas.harvard.edu
SUMMARY:Learning and inference from sensitive data
DESCRIPTION:Speaker: Adam 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.
URL:https://cmsa.fas.harvard.edu/event/learning-and-inference-from-sensitive-data/
LOCATION:Virtual
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-02.02.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220201T093000
DTEND;TZID=America/New_York:20220201T103000
DTSTAMP:20260516T065125
CREATED:20230818T053619Z
LAST-MODIFIED:20240304T064710Z
UID:10001288-1643707800-1643711400@cmsa.fas.harvard.edu
SUMMARY:Curve-counting with fixed domain (“Tevelev degrees”)
DESCRIPTION:Abstract: We will consider the following problem: if (C\,x_1\,…\,x_n) is a fixed general pointed curve\, and X is a fixed target variety with general points y_1\,…\,y_n\, then how many maps f:C -> X in a given homology class are there\, such that f(x_i)=y_i? When considered virtually in Gromov-Witten theory\, the answer may be expressed in terms of the quantum cohomology of X\, leading to explicit formulas in some cases (Buch-Pandharipande). The geometric question is more subtle\, though in the presence of sufficient positivity\, it is expected that the virtual answers are enumerative. I will give an overview of recent progress on various aspects of this problem\, including joint work with Farkas\, Pandharipande\, and Cela\, as well as work of other authors.
URL:https://cmsa.fas.harvard.edu/event/curve-counting-with-fixed-domain-tevelev-degrees/
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-02.01.2022-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220131T130000
DTEND;TZID=America/New_York:20220131T140000
DTSTAMP:20260516T065125
CREATED:20240214T110850Z
LAST-MODIFIED:20240301T074639Z
UID:10002691-1643634000-1643637600@cmsa.fas.harvard.edu
SUMMARY:Membrane Limits in Quantum Gravity
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/1-31-2022-swampland-seminar/
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220128T143000
DTEND;TZID=America/New_York:20220128T160000
DTSTAMP:20260516T065125
CREATED:20240214T111332Z
LAST-MODIFIED:20240301T074750Z
UID:10002692-1643380200-1643385600@cmsa.fas.harvard.edu
SUMMARY:Maximal quantum chaos of the critical Fermi surface
DESCRIPTION:Speaker: Maria Tikhanovskaya (Harvard) \nTitle: Maximal quantum chaos of the critical Fermi surface \nAbstract: In this talk\, I will describe many-body quantum chaos in a recently proposed large-N theory for critical Fermi surfaces in two spatial dimensions\, by computing out-of-time-order correlation functions. I will use the ladder identity proposed by Gu and Kitaev\, and show that the chaos Lyapunov exponent in this system takes on the maximum possible value of 2πkBT/ℏ\, where T is the absolute temperature. In addition\, by varying the dynamic critical exponent\, I will show that the maximal chaos persists only in the regime where quasiparticles are absent. When quasiparticles are present\, the Lyapunov exponent scales with the temperature as ~ T^a\, where a < 1\, which is parametrically smaller than the maximal rate.
URL:https://cmsa.fas.harvard.edu/event/1-28-2022-quantum-matter-in-mathematics-and-physics/
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-1.28.2022-1544x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220128T093000
DTEND;TZID=America/New_York:20220128T103000
DTSTAMP:20260516T065125
CREATED:20240214T090436Z
LAST-MODIFIED:20240301T112154Z
UID:10002605-1643362200-1643365800@cmsa.fas.harvard.edu
SUMMARY:Singular Calabi-Yau mirror symmetry
DESCRIPTION:Speaker: Bong Lian \nTitle: Singular Calabi-Yau mirror symmetry \nAbstract: We will consider a class of Calabi-Yau varieties given by cyclic branched covers of a fixed semi Fano manifold. The first prototype example goes back to Euler\, Gauss and Legendre\, who considered 2-fold covers of P1 branched over 4 points. Two-fold covers of P2 branched over 6 lines have been studied more recently by many authors\, including Matsumoto\, Sasaki\, Yoshida and others\, mainly from the viewpoint of their moduli spaces and their comparisons.  I will outline a higher dimensional generalization from the viewpoint of mirror symmetry. We will introduce a new compactification of the moduli space cyclic covers\, using the idea of ‘abelian gauge fixing’ and ‘fractional complete intersections’. This produces a moduli problem that is amenable to tools in toric geometry\, particularly those that we have developed jointly in the mid-90’s with S. Hosono and S.-T. Yau in our study of toric Calabi-Yau complete intersections. In dimension 2\, this construction gives rise to new and interesting identities of modular forms and mirror maps associated to certain K3 surfaces. We also present an essentially complete mirror theory in dimension 3\, and discuss generalization to higher dimensions. The lecture is based on joint work with Shinobu Hosono\, Tsung-Ju Lee\, Hiromichi Takagi\, Shing-Tung Yau.
URL:https://cmsa.fas.harvard.edu/event/1-28-2022-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220127T145400
DTEND;TZID=America/New_York:20220127T165400
DTSTAMP:20260516T065125
CREATED:20240215T092855Z
LAST-MODIFIED:20240215T092855Z
UID:10002718-1643295240-1643302440@cmsa.fas.harvard.edu
SUMMARY:1/27/2022 – Interdisciplinary Science Seminar
DESCRIPTION:Title: Polynomials vanishing at lattice points in convex sets \nAbstract: Let P be a convex subset of R^2. For large d\, what is the smallest degree r_d of a polynomial vanishing at all lattice points in the dilate d*P? We show that r_d / d converges to some positive number\, which we compute for many (but maybe not all) triangles P.
URL:https://cmsa.fas.harvard.edu/event/1-27-2022-interdisciplinary-science-seminar/
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-1.27.2022-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220127T130000
DTEND;TZID=America/New_York:20220127T143000
DTSTAMP:20260516T065125
CREATED:20230824T171841Z
LAST-MODIFIED:20240304T083455Z
UID:10001306-1643288400-1643293800@cmsa.fas.harvard.edu
SUMMARY:Learning to School in the presence of hydrodynamic interactions
DESCRIPTION:Abstract: Fluids pervade complex systems\, ranging from fish schools\, to bacterial colonies and nanoparticles in drug delivery. Despite its importance\, little is known about the role of fluid mechanics in such applications. Is schooling the result of vortex dynamics synthesized by individual fish wakes or the result of behavioral traits? Is fish schooling energetically favorable?  I will present multifidelity computational studies of collective swimming in 2D and 3D flows. Our studies demonstrate that classical models of collective swimming (like the Reynolds model) fail to maintain coherence in the presence of long-range hydrodynamic interactions. We demonstrate in turn that collective swimming can be achieved through reinforcement learning. We extend these studies to 2D and 3D viscous flows governed by the Navier Stokes equations. We examine various hydrodynamic benefits with a progressive increase of the school size and demonstrate the importance of controlling the vorticity field generated by up to 300 synchronized swimmers.
URL:https://cmsa.fas.harvard.edu/event/learning-to-school-in-the-presence-of-hydrodynamic-interactions/
CATEGORIES:Active Matter Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Active-Matter-Seminar-01.27.2022-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220126T140000
DTEND;TZID=America/New_York:20220126T150000
DTSTAMP:20260516T065125
CREATED:20230808T180637Z
LAST-MODIFIED:20240517T193321Z
UID:10001203-1643205600-1643209200@cmsa.fas.harvard.edu
SUMMARY:Machine learning with mathematicians
DESCRIPTION:Speaker: Alex Davies\, DeepMind \nTitle: Machine learning with mathematicians \nAbstract: Can machine learning be a useful tool for research mathematicians? There are many examples of mathematicians pioneering new technologies to aid our understanding of the mathematical world: using very early computers to help formulate the Birch and Swinnerton-Dyer conjecture and using computer aid to prove the four colour theorem are among the most notable. Up until now there hasn’t been significant use of machine learning in the field and it hasn’t been clear where it might be useful for the questions that mathematicians care about. In this talk we will discuss the results of our recent Nature paper\, where we worked together with top mathematicians to use machine learning to achieve two new results – proving a new connection between the hyperbolic and geometric structure of knots\, and conjecturing a resolution to a 50-year problem in representation theory\, the combinatorial invariance conjecture. Through these examples we demonstrate a way that machine learning can be used by mathematicians to help guide the development of surprising and beautiful new conjectures.
URL:https://cmsa.fas.harvard.edu/event/1-26-2022-new-technologies-in-mathematics/
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-Seminar-01.26.2022-1553x2048-1.jpg
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