This biweekly online colloquium features geometers and physicists presenting current research on a wide range of topics in the interface of the two fields. The talks are aimed at a broad audience. They will take place via Zoom on alternate Mondays at 3pm Eastern, noon Pacific, 5pm BRT. Each session features a 60 minute talk, followed by 15 minutes for questions and discussion. You may join the meeting 15 minutes in advance. Questions and comments may be submitted to the moderator via the chat interface during the talk, or presented in person during the Q&A session. These colloquia will be recorded and will be available (linked from this page) asap after the event.
As an alternative to Zoom, you may watch a live stream of the lecture at our: YouTube streaming site.
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Organizing committee: Tudor Dimofte, Ron Donagi, Dan Freed, Sheldon Katz, Dave Morrison, Andy Neitzke.
(Indexed at researchseminars.org.)
Go to Past Talks (2020). Past Talks (2021) Past Talks (2022) Past Talks (2023)Marh 27, 2023 
Sakura SchaferNameki (Oxford)Title TBAAbstract: 
April 10, 2023 
Guangbo Xu (Texas A&M)Title TBAAbstract: 
April 24, 2023 
Pavel Safronov (Edinburgh)Title TBAAbstract: 
May 8, 2023 
Sam Raskin (UT Austin)Title TBAAbstract: 
January 30, 2023 
Xin Sun (University of Pennsylvania)Random surfaces, planar lattice models, and conformal field theoryAbstract: Liouville quantum gravity (LQG) is a theory of random surfaces that originated from string theory. Schramm Loewner evolution (SLE) is a family of random planar curves describing scaling limits of many 2D lattice models at their criticality. Before the rigorous study via LQG and SLE in probability, random surfaces and scaling limits of lattice models have been studied via another approach in theoretical physics called conformal field theory (CFT) since the 1980s. In this talk, I will demonstrate how a combination of ideas from LQG/SLE and CFT can be used to rigorously prove several long standing predictions in physics on random surfaces and planar lattice models, including the law of the random modulus of the scaling limit of uniform triangulation of the annular topology, and the crossing formula for critical planar percolation on an annulus. I will then present some conjectures which further illustrate the deep and rich interaction between LQG/SLE and CFT. Based on joint works with Ang, Holden, Remy, Xu, and Zhuang. Video of lecture 
February 13, 2023 
Thomas Grimm (Utrecht)The Tameness of Quantum PhysicsAbstract: While physicists have learned to accept the many wild phenomena of quantum theories, one might hope that the mathematical structure underlying these theories is more tame and inherently geometric in nature. The aim of this colloquium is to introduce a general tameness principle, using ominimal structures originating in mathematical logic, and argue that it is common to many welldefined quantum theories. We will discuss quantum field theories and show the tameness of perturbative scattering amplitudes. At the nonperturbative level, tameness depends on the highenergy definition of the physical theory and might be seen as a condition that arises from consistency with quantum gravity. In fact, all wellunderstood effective theories derived from string theory appear to be tame. As one direct application we will see how this property is key in the mathematical proof of an almost 20yearold finiteness conjecture for string theory vacua. We will close by formulating our expectations on the tameness of conformal field theories and their observables. Video of lecture OR Video of lecture (alternate version, same content as the other) 
February 27, 2023 
Marcos Marino (Geneva)Resurgence and nonperturbative topological stringsAbstract: The theory of resurgence provides a precise and unified mathematical formulation of the nonperturbative sectors of a physical theory, based solely on its perturbative expansion. In recent years it has been applied to topological quantum field theories and topological strings, leading to many insights and results. For example, it has been found that, in many cases, the Stokes constants appearing in resurgent analysis are related to BPS invariants. In this talk I will first review the resurgence program in topological theories, and then I will consider recent progress on its implementation in topological string theories. To do this, I introduce the analogue of instanton calculus in KodairaSpencer theory, based on transseries solutions to the holomorphic anomaly equations. This leads to exact, (spacetime) multiinstanton amplitudes of the topological string on arbitrary CalabiYau manifolds, and gives nonperturbative corrections in the string coupling constant. These results also suggest that, in the full quantum theory, the moduli of the CalabiYau are quantized in units of the string coupling constant. As an application of these results, I present the allorders, large genus asymptotics for the topological string free energies on the famous quintic CalabiYau. Video of lecture OR Video of lecture (alternate version, same content as the other) 
March 13, 2023 
Clark Barwick (Edinburgh)Condensed/pyknotic structures: a gentle introductionAbstract: Condensed (alias pyknotic) structures provide a formalism in which algebraic structures can interact gracefully with topological structures. I will introduce the ideas via some simple examples. If time permits, I will explain how these structures arise when one contemplates field theories in padic contexts. Video of lecture OR Video of lecture (alternate version, same content as the other) 
January 24, 2022 
Hirosi Ooguri (Cal Tech/Kavli IPMU)Symmetry in QFT and GravityAbstract: I will review aspects of symmetry in quantum field theory and combine them with the AdS/CFT correspondence to derive constraints on symmetry in quantum gravity. The quantum gravity constraints to be discussed include the nogo theorem on global symmetry, the completeness of gauge charges, and the decomposition of high energy states into gauge group representations. OR Video of lecture (alternate version, same content as the other) 
February 7, 2022 
Emily Cliff (Université de Sherbrooke)Moduli spaces of principal 2group bundles and a categorification of the FreedQuinn line bundleAbstract: A 2group is a higher categorical analogue of a group, while a smooth 2group is a higher categorical analogue of a Lie group. An important example is the string 2group in the sense of SchommerPries. We study the notion of principal bundles for smooth 2groups, and investigate the moduli "space" of such objects. In particular in the case of flat principal bundles for a finite 2group over a Riemann surface, we prove that the moduli space gives a categorification of the FreedQuinn line bundle. This line bundle has as its global sections the state space of ChernSimons theory for the underlying finite group. We can also use our results to better understand the notion of geometric string structures (as previously studied by Waldorf and StolzTeichner). This is based on joint work with Dan BerwickEvans, Laura Murray, Apurva Nakade, and Emma Phillips.
Video of lecture OR Video of lecture (alternate version, same content as the other) 
February 28, 2022 
Eric Zaslow (Northwestern)Framing DualityAbstract: I will describe joint work in progress with Linhui Shen and Gus Schrader, in which we study moduli spaces of Fukaya objects and conjecture about their relationship to BPS and open GromovWitten invariants. This unabashedly synthesize previous works of many other groups, whom I will credit in the talk. I will try to highlight some new aspects: 1) a definition of phases and framings and their combinatorial origins; 2) conjectures on open GromovWitten invariants for Lagrangians bounding certain Legendrian surfaces; 3) a “framing duality” relating DondaldsonThomas and open GromovWitten invariants.
Video of lecture OR Video of lecture (alternate version, same content as the other) 
March 14, 2022 
Joerg Teschner (DESY)The complex geometry of topological string partition functionsAbstract: The goal of this talk will be to review some aspects of a program inspired by work of Tom Bridgeland aiming at a nonperturbative characterisation of topological string partition functions. The program is based on two main ingredients: The complex geometry of the underlying moduli spaces on the one hand, and cluster algebra structures defined by BPS or DTinvariants on the other hand. The general picture is nicely illustrated by the Borel summation of the conifold partition functions recently studied with M. Alim, A. Saha and I. Tulli, with Stokes jumps of the partition functions getting related to wallcrossing phenomena in the theory of DTinvariants. Based on this and other examples we will propose a conjectural characterisation of the partition functions for local CalabiYau manifolds, generalising earlier proposals by Marino and collaborators, and related to earlier proposals by Alexandrov, Pioline and collaborators based on the geometry of hypermultiplet moduli spaces.
Video of lecture OR Video of lecture (alternate version, same content as the other) 
March 28, 2022 
Washington Taylor (MIT)Middle intersection forms on singular elliptic CalabiYau fourfolds, and applications to the standard model and mirror symmetryAbstract: Recent work with Jefferson and Turner indicates that the intersection form on the vertical part of middle cohomology of singular elliptic CalabiYau fourfolds is independent of resolution. This suggests that the intersection structure should have a natural definition even in these singular geometries. The resulting intersection form has a simple blockdiagonal structure in terms of Kodaira singularities and the geometry of the base of the elliptic fibration; the talk will describe applications of this intersection form to analysis of chiral matter and standard model constructions in Ftheory as well as new insights into mirror symmetry, in particular providing in some cases a complete description of the intersection form on H_4 (X, Z) for a smooth CalabiYau fourfold including both vertical and horizontal parts. Video of lecture OR Video of lecture (alternate version, same content as the other) 
April 11, 2022 
Daniel HalpernLeistner (Cornell)Infinite dimensional geometric invariant theory and gauged GromovWitten theoryAbstract: HarderNarasimhan (HN) theory gives a structure theorem for holomorphic vector bundles on a Riemann surface. A bundle is either semistable, or it admits a canonical filtration whose associated graded bundle is semistable in a graded sense. After reviewing recent advances in extending HN theory to arbitrary moduli problems in algebraic geometry I will discuss work in progress with Andres Fernandez Herrero and Eduardo Gonzalez to apply this general machinery to the moduli problem of gauged maps from a curve C to a Gvariety X, where G is a reductive group. Our main immediate application is to use HN theory for gauged maps to compute generating functions for Ktheoretic gauged GromovWitten invariants. This problem is interesting more broadly because it can be formulated as an example of an infinite dimensional analog of the usual set up of geometric invariant theory, which has applications to other moduli problems.
Video of lecture OR Video of lecture (alternate version, same content as the other) 
April 25, 2022 
Constantin Teleman (U.C. Berkeley)Coulomb branches and Drinfeld centersAbstract: We discuss a construction of Coulomb branches of a compact Lie group G from the Toda integrable systems and speculate on their origins as Drinfeld centers of modifications of (a variant of) the tensor category of topological representations of G. Video of Lecture OR Video of lecture (alternate version, same content as the other) 
May 9, 2022 
Heeyeon Kim (Rutgers University)Path integral derivations of Ktheoretic Donaldson invariantsAbstract: We discuss path integral derivations of topologically twisted partition functions of 5d SU(2) supersymmetric YangMills theory on M4 x S1, where M4 is a smooth closed fourmanifold. Mathematically, they can be identified with the Ktheoretic version of the Donaldson invariants. In particular, we provide two different path integral derivations of their wallcrossing formula for b_2^+(M4)=1, first in the socalled Uplane integral approach, and in the perspective of instanton counting. We briefly discuss the generalization to b_2^+(M4)>1.
Video of lecture OR Video of lecture (alternate version, same content as the other) 
September 12, 2022 
Edward Witten (Institute for Advanced Study)An Algebra of Observables for de Sitter SpaceAbstract: De Sitter space is the maximally symmetric solution of Einstein's equations with positive cosmological constant. It is also perhaps the simplest example of a spacetime with a cosmological horizon, and this, as explained long ago by Gibbons and Hawking, leads to perplexing questions about quantum field theory and gravity in a de Sitter spacetime. I will describe a von Neumann algebra of Type II_1 that describes the observations made by an observer in de Sitter space. This provides an abstract answer to some of the questions.
Video of lecture OR Video of lecture (alternate version, same content as the other) 
October 3, 2022 
Ciprian Manolescu (Stanford University)What is a Floer homotopy type?Abstract: Floer homology is an important tool in both symplectic geometry and lowdimensional topology. I will briefly review the different versions of Floer homology (Hamiltonian, Lagrangian, YangMills, SeibergWitten, Khovanov), and then describe the program to refining them by producing (stable) homotopy types whose homology is Floer homology. Among the applications of the resulting Floer homotopy are a proof of the existence of nontriangulable manifolds in high dimensions (due to the presenter) and the recent proof of the Arnold conjecture with Z/p coefficients (due to Abouzaid and Blumberg). Recommended reference: "Floer homotopy theory, revisited" by Ralph Cohen, https://arxiv.org/pdf/1901.08694.pdf
Video of lecture OR Video of lecture (alternate version, same content as the other) 
October 17, 2022 
Mike Douglas (Harvard CMSA)How will we do mathematics in 2030 ?Abstract: We make the case that over the coming decade, computer assisted reasoning will become far more widely used in the mathematical sciences. This includes interactive and automatic theorem verification, symbolic algebra, and emerging technologies such as formal knowledge repositories, semantic search and intelligent textbooks. After a short review of the state of the art, we survey directions where we expect progress, such as mathematical search and formal abstracts, developments in computational mathematics, integration of computation into textbooks, and organizing and verifying large calculations and proofs. For each we try to identify the barriers and potential solutions.
Video of lecture OR Video of lecture (alternate version, same content as the other) 
October 31, 2022 
Herman Verlinde (Princeton)Sduality and Mirror Symmetry in TTbar deformed CFTAbstract: After a brief review of TTbar conformal field theory, I will study the grandcanonical partition sum of TTbar deformed symmetric product CFT. We will find that it admits a natural extension that exhibits an Sduality symmetry under an PSL(2,Z)duality group that exchanges strong and weak TTbar coupling, and an analog of mirror symmetry that exchanges to modular shape of the torus with the complexified TTbar coupling. Video of lecture OR Video of lecture (alternate version, same content as the other) 
November 14, 2022 
Sara Pasquetti (University of Milan, Bicocca)The local dualisation algorithm at workAbstract: I will present an algorithm to construct mirror and more general SL(2,Z) duals of 3d N=4 quiver theories and of their 4d uplifts. The algorithm uses a set of basic duality moves and the properties of the dualitywalls providing a generalisation of the KapustinStrassler local dualisation to the nonabelian case. All the basic duality moves can be derived by iterative applications of Seiberglike dualities, hence our algorithm implies that mirror and SL(2,Z) dualities can be derived assuming only Seiberg duality. I will also discuss the case of bad theories, where the dualisation algorithm allows us to extract nontrivial information on the quantum moduli space. Video of lecture OR Video of lecture (alternate version, same content as the other) 
November 28, 2022 
Dalimil Mazac (IAS)Automorphic Spectra and the Conformal BootstrapAbstract: I will describe a close analogy between the spectral geometry of hyperbolic manifolds and conformal field theory. A hyperbolic dmanifold gives rise to a Hilbert space which is a unitary representation of the conformal group in d1 dimensions. Elements of this Hilbert space can be thought of as local operators living in a (d1)dimensional spacetime. Their scaling dimensions are related to the Laplacian eigenvalues on the manifold. The operators satisfy an operator product expansion. One can define correlation functions and derive conformal bootstrap equations constraining the spectrum. As an application, I will use conformal bootstrap techniques to obtain new rigorous bounds on the first positive Laplacian eigenvalue of hyperbolic orbifolds. In two dimensions, these bounds allow us to determine the set of first eigenvalues attained by all hyperbolic orbifolds. Based on joint work with Petr Kravchuk and Sridip Pal and ongoing work with James Bonifacio. Video of lecture OR Video of lecture (alternate version, same content as the other) 
December 12, 2022 
Natalie Paquette (University of Washington)Koszul duality & twisted holography for asymptotically flat spacetimesAbstract: Koszul duality has been understood in recent years to characterize ordertype defects in twists of supersymmetric field theories. This notion has been generalized, from a physical point of view, by studying couplings between Dbranes and closed string theories in the topological string. Computing the Dbrane backreaction, and studying the resulting open/closed string duality, is the purview of the twisted holography program. Twisted holography seeks to study supersymmetric sectors of the AdS/CFT correspondence using these methods, and leverage the appropriate generalization of Koszul duality to elucidate the bulk/boundary map. When applying these methods to a topological string configuration on twistor space, one can construct an instance of twisted holography in which a 2d chiral algebra, supported on the ``celestial sphere'', is dual to a 4d theory in an asymptotically flat spacetime. This is the first such topdown example of holography in an asymptotically flat spacetime. This talk describes joint work done, variously, with Kevin Costello, Brian Williams, and Atul Sharma. 
January 11, 2021 
Mike Freedman (Microsoft Research/UCSB)Quantum Codes and Systolic freedomAbstract: In work with Hastings we find a twoway street between quantum error correcting codes and Riemannian manifolds. A recent advance in coding theory allows us to produce the first example of a manifolds with Z_2power lawsystolic freedom. Specifically we find, for any e>0, a sequence of appropriately scaled 11D Riemannian manifolds M_i, so that for any dual 4 and 7 dimensional Z_2cycles, X_i and Y_i, resp. $ Vol_4(X_i)*Vol_7(Y_i) > (Vol_11(M_i))^(5/4e) $. Video of lecture

January 25, 2021 
Albrecht Klemm (Bonn)CalabiYau modularity and Feynman GraphsAbstract: Using the GKZ system for the primitive cohomology of an infinite series of complete intersection CalabiYau manifolds, whose dimension is the loop order minus one, we completely clarify the analytic structure of all banana integrals with arbitrary masses. In particular, we find that the leading logarithmic structure in the high energy regime, which corresponds to the point of maximal unipotent monodromy, is determined by a novel \hat bclass evaluation in the ambient spaces of the mirror, while the imaginary part of the amplitude in this regime is determined by the Γbclass of the mirror CalabiYau manifold itself. We provide simple closed all loop formulas for the former as well as for the Frobenius κconstants, which determine the behaviour of the amplitudes, when the momentum square equals the sum of the masses squared, in terms of zeta values. We find the exact differential equation for the graph integrals with arbitrary value for the dimensional regularisation (d\epsilon) parameter and extend our previous work from three to four loops by providing for the latter case a complete set of (inhomogenous) PicardFuchs differential ideal for arbitrary masses. Using a recent padic analysis of the periods we determine the value of the maximal cut equal mass fourloop amplitude at the attractor points in terms of periods of modular weight two and four Hecke eigenforms and the quasiperiods of their meromorphic cousins. Video of lecture 
February 8, 2021 
Nikita Nekrasov (SCGP, Stony Brook)Beauty of the defectsAbstract: Surface and pointlike defects in supersymmetric gauge theories in four dimensions are studied with applications to quantum/classical correspondence. In particular, the GIL formula for the taufunction of Painleve VI is explained using the blowup method in the context of the BPS/CFT correspondence, while the spin chain generalisation of KharchevLebedev wavefunction of periodic Toda chain is obtained via wallcrossing. Based on several works, in particular on papers in collaboration with Saebyeok Jeong; Norton Lee; Oleksandr Tsymbaliuk; as well as S. Jeong and N. Lee Video of lecture 
February 22, 2021 
Tamas Hausel (IST Austria)Mirror symmetry for Langlands dual Higgs bundles at the tip of the nilpotent coneAbstract: I will explain what we can prove and what we conjecture about the mirror of Hecke transformed Hitchin section motivated by symmetry ideas of KapustinWitten. The talk is based on arXiv:2101.08583 joint with Hitchin. 
March 8, 2021 
Thomas Dumitrescu (UCLA)2Group Global Symmetry in Quantum Field TheoryAbstract: Higherform generalizations of global symmetries play an important role in Quantum Field Theory (QFT). In general, symmetries of different form degrees need not be independent; instead, they can form a higher group. In this talk I will illustrate this phenomenon by explaining why many simple Lagrangian QFTs in four and six dimensions enjoy 2group global symmetries. I will then apply this understanding to deduce new general results about (typically nonLagrangian) SCFTs in six dimensions. 
March 22, 2021 
David BenZvi (U. Texas, Austin)ElectricMagnetic Duality between Periods and LfunctionsAbstract: I will describe joint work with Yiannis Sakellaridis and Akshay Venkatesh, in which ideas originating in quantum field theory are applied to a problem in number theory. A fundamental tool in number theory, the relative Langlands program, is centered on the representation of Lfunctions of Galois representations as integrals of automorphic forms. However, the data that naturally index these period integrals (spherical varieties for a reductive group G) and the Lfunctions (representations of the Langlands dual group G^) don't seem to line up, making the search for integral representations somewhat of an art. We present an approach to this problem via the KapustinWitten interpretation of the [geometric] Langlands correspondence as electricmagnetic duality for 4dimensional supersymmetric gauge theory. Namely, we rewrite the relative Langlands program as duality in the presence of boundary conditions. As a result the partial correspondence between periods and Lfunctions is embedded in a natural duality between Hamiltonian actions of the dual groups. 
April 5, 2021 
Arnav Tripathy (Harvard)K3 metricsIt has long been an open problem to explicitly produce a Ricciflat metric on a (nontoroidal) compact manifold. I'll discuss two approaches to this problem, related by a version of 3d mirror symmetry, for K3 manifolds. This is joint work with M. Zimet. 
April 19, 2021 
Cody Long and Cumrun Vafa (Harvard)NonHolomorphic Cycles and NonBPS Black BranesAbstract: We discuss extremal nonBPS black holes and strings arising in Mtheory compactifications on CalabiYau threefolds, obtained by wrapping M2 branes on nonholomorphic 2cycles and M5 branes on nonholomorphic 4cycles. Using the attractor mechanism we compute the black hole mass and black string tension, leading to a conjectural formula for the asymptotic volumes of connected, locally volumeminimizing representatives of nonholomorphic, evendimensional homology classes in the threefold, without knowledge of an explicit metric. In the case of divisors we find examples where the volume of the representative corresponding to the black string is less than the volume of the minimal piecewiseholomorphic representative, predicting recombination for those homology classes and leading to stable, nonBPS strings. We also show how to compute the central charges of nonBPS strings in Ftheory via a nearhorizon AdS3 limit in 6d which, upon compactification on a circle, account for the asymptotic entropy of extremal nonsupersymmetric 5d black holes (i.e., the asymptotic count of nonholomorphic minimal 2cycles). Video of lecture 
May 3, 2021 
Fei Yan (Rutgers)Two tales of networks and quantizationAbstract: I will describe two quantization scenarios. The first scenario involves the construction of a quantum trace map computing a new link "invariant" (with possible wallcrossing behavior) for links L in a 3manifold M, where M is a Riemann surface C times a real line. This construction computes familiar link invariants in a new way, moreover it unifies that computation with the computation of protected spin characters counting ground states with spin for line defects in 4d N=2 theories of classS. Certain networks on C play an important role in the construction. The second scenario concerns the study of Schroedinger equations and their higher order analogues, which could arise in the quantization of SeibergWitten curves in 4d N=2 theories. Here similarly certain networks play an important part in the exact WKB analysis for these Schroedingerlike equations. At the end of my talk I will also try to sketch a possibility to bridge these two quantization scenarios. The first part of the talk is based on joint work with A. Neitzke; the final sketch is based on discussions with D. Gaiotto, G. Moore and A. Neitzke. 
May 17, 2021 
Richard Thomas (Imperial College)Nonabelian DT theory from abelian DT theoryAbstract: Fix a CalabiYau 3fold X. Its DT invariants count stable bundles and sheaves on X. Joyce's generalised DT invariants count semistable sheaves on X. I will describe ongoing work with Soheyla Feyzbakhsh with the eventual aim of writing the generalised DT invariants in any rank r in terms of rank 1 invariants. By the MNOP conjecture the latter are determined by the GW invariants of X. Along the way we express rank r DT invariants in terms of rank 0 invariants counting D4D2D0 branes. These invariants are predicted by Sduality to be governed by (vectorvalued mock) modular forms. Based partly on arXiv:2007.03037 and arXiv:2103.02915 . 
June 7, 2021 
Zohar Komargodski (SCGP, Stony Brook)Higher central charges and gapped boundariesAbstract: The chiral central charge is a famous diagnostic of edge modes on the boundary of 2+1 dimensional topological phases. We show that many theories with a vanishing chiral central charge nevertheless cannot admit a gapped boundary. We define higher chiral central charges and investigate their properties. 
June 21, 2021 
no meeting, due to Strings 2021

July 12, 2021 
Sarah Harrison (McGill)New BPS algebras from superstring compactificationsAbstract: Borcherds KacMoody (BKM) algebras are a generalization of familiar KacMoody algebras with imaginary simple roots. On the one hand, they were invented by Borcherds in his proof of the monstrous moonshine conjectures and have many interesting connections to new moonshines, number theory and the theory of automorphic forms. On the other hand, there is an old conjecture of Harvey and Moore that BPS states in string theory form an algebra that is in some cases a BKM algebra and which is based on certain signatures of BKMs observed in 4d threshold corrections and black hole physics. I will briefly review the construction of new BKMs superalgebras arising from selfdual vertex operator algebras of central charge 12, and then discuss recent work showing how they arise as algebras of BPS states in physical string theories in 2 dimensions, as well as their connection with automorphic forms. Based on work with N. Paquette, D. Persson, and R. Volpato. This can be seen as a followup to a talk given by N. Paquette at this series this past October. 
July 26, 2021 
Theo JohnsonFreyd (Perimeter/Dalhousie)Semisimple higher categoriesAbstract: Semisimple higher categories are a quantum version of topological spaces (behaving sometimes like homotopy types and sometimes like manifolds) in which cells are attached along superpositions of other cells. Many operations from topology make sense for semisimple higher categories: they have homotopy sets (not groups), loop spaces, etc. For example, the extended operators in a topological sigma model form a semisimple higher category that can be thought of as a type of "cotangent bundle" of the target space. The "symplectic pairing" on this "cotangent bundle" is measured an Smatrix pairing aka Whitehead bracket defined on the homotopy sets of any (pointed connected) semisimple higher category, and the nondegeneracy of this pairing is a type of Poincare or Atiyah duality. This is joint work in progress with David Reutter.
Video of lecture OR Video of lecture (alternate version, same content as the other) 
September 13, 2021 
Pavel Etingof (MIT)Hecke operators over local fields and an analytic approach to the geometric Langlands correspondenceAbstract: I will review an analytic approach to the geometric Langlands correspondence, following my work with E. Frenkel and D. Kazhdan, arXiv:1908.09677, arXiv:2103.01509, arXiv:2106.05243. This approach was developed by us in the last couple of years and involves ideas from previous and ongoing works of a number of mathematicians and mathematical physicists, Kontsevich, Langlands, Teschner, and GaiottoWitten. One of the goals of this approach is to understand singlevalued real analytic eigenfunctions of the quantum Hitchin integrable system. The main method of studying these functions is realizing them as the eigenbasis for certain compact normal commuting integral operators the Hilbert space of L2 halfdensities on the (complex points of) the moduli space Bun_G of principal Gbundles on a smooth projective curve X, possibly with parabolic points. These operators actually make sense over any local field, and over nonarchimedian fields are a replacement for the quantum Hitchin system. We conjecture them to be compact and prove this conjecture in the genus zero case (with parabolic points) for G=PGL(2). I will first discuss the simplest nontrivial example of Hecke operators over local fields, namely G=PGL(2) and genus 0 curve with 4 parabolic points. In this case the moduli space of semistable bundles Bun_G^{ss} is P^1, and the situation is relatively well understood; over C it is the theory of singlevalued eigenfunctions of the Lame operator with coupling parameter 1/2 (previously studied by Beukers and later in a more functionalanalytic sense in our work with Frenkel and Kazhdan). I will consider the corresponding spectral theory and then explain its generalization to N>4 points and conjecturally to higher genus curves.
Video of Lecture OR Video of lecture (alternate version, same content as the other) Slides of Lecture (first part); link to Slides of Lecture (second part) 
September 27, 2021 
Nathan Seiberg (IAS)Comments on Lattice vs. Continuum Quantum Field TheoryAbstract: There is an interesting interplay between continuum quantum field theory (QFT) and lattice systems. First, as in condensedmatter physics, we start at short distances (UV) with a lattice model and our goal is to find its long distance (IR) behavior. The lore is that this behavior is captured by a continuum QFT. Conversely, as is more common in highenergy physics and mathematical physics, the lattice theory is a first step toward a rigorous definition of the continuum theory. Despite enormous progress over the past decades, these two directions of the interplay between the lattice and the continuum face interesting challenges. Here, motivated by recently discovered theoretical phases of matter (including the XYplaquette model and models of fractons), we will address two aspects of the relation between the lattice in the UV and the continuum in the IR. We will present lattice models exhibiting topological properties of continuum theories, like winding symmetries, ‘t Hooft anomalies, and duality. We will use this approach to clarify the subsystem global symmetries of some of the recently discovered exotic models. We will also discuss some more dynamical aspects of these systems and in particular their enigmatic UV/IR mixing; i.e., some longdistance properties are sensitive to shortdistance details. Video of Lecture OR Video of lecture (alternate version, same content as the other) 
October 11, 2021 
Ryan Thorngren (Harvard University)A Tour of Categorical SymmetryAbstract: A categorical symmetry is a category acting as a symmetry of a QFT. These symmetries correspond to the topological operators in the QFT. I'll try to motivate this definition with some simple examples. Then I'll discuss a bulkboundary correspondence which in finite situations allows us to classify gapped phases with categorical symmetry and define things like anomalous symmetries and gauging. I'll conclude with some more examples of topological operators in c = 1 CFTs and describe a Noether theorem for continuous categorical symmetries. Video of lecture OR Video of lecture (alternate version, same content as the other) 
October 25, 2021 
Ibrahima Bah (Johns Hopkins University)Nonsupersymmetric smooth solitonic solutions in EinsteinMaxwell type theoriesAbstract: In this talk I will present a recent framework to construct and study smooth horizonless nonsupersymmetric solutions in gravity with interesting topologies. These live in backgrounds that are 4d Minkowski with tori of various dimensions. I will discuss the physical mechanism that allows for their existence and comment on their classical and thermodynamic stability. I will describe a family of these constructions that resolve certain curvature singularities. Video of lecture OR Video of lecture (alternate version, same content as the other) 
November 8, 2021 
Tony Pantev (University of Pennsylania)Geometry and topology of wild character varietiesAbstract: Wild character varieties parametrize monodromy representations of flat meromorphic connections on compact Riemann surfaces. They are classical objects with remarkable geometric and topological properties. I will recall how intrinsic geometric structures resolve singularities of wild character varieties and will show that their algebraic symplectic structures extend naturally to the resolutions. This is based on a new universal method for producing symplectic structures which is a joint work with Arinkin and Toen. I will also describe recent joint works with Chuang, Diaconescu, Donagi, and Nawata in which we use string dualities to extract cohomological invariants of twisted wild character varieties from BPS counts on CalabiYau threefolds and refined ChernSimons invariants of torus knots. Video of lecture OR Video of lecture (alternate version, same content as the other) 
November 22, 2021 
Lotte Hollands (HeriotWatt University)Partition functions, BPS states and abelianizationAbstract: In this talk I will reexpress the NekrasovShatashvili partition function for a fourdimensional N=2 gauge theory as an integral of a ratio of Wronskians of solutions to the relevant oper equation, with the AD2 theory and the pure SU(2) theory as two main examples. This motivates the definition of a generalized NekrasovShatashvili partition function for any fourdimensional N=2 theory of class S, and makes a connection with abelianization and exact WKB analysis. We will end with some remarks regarding the fivedimensional generalization and the relation to similar mathematical structures underlying the topological string partition function. This talk is based on 2109.14699 and work in progress. Video of Lecture OR Video of lecture (alternate version, same content as the other) 
December 6, 2021 
Clay Córdova (University of Chicago)NonInvertible Duality DefectsAbstract: For any quantum system invariant under gauging a higherform global symmetry, we construct a noninvertible topological defect by gauging in only half of spacetime. This generalizes the KramersWannier duality line in 1+1 dimensions to higher space time dimensions. We focus on the case of a oneform symmetry in 3+1 dimensions, and determine the fusion rule. From a direct analysis of oneform symmetry protected topological phases, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. We give an explicit realization of this duality defect in the free Maxwell theory where it is realized by a ChernSimons coupling between the gauge fields from the two sides. Video of Lecture OR Video of lecture (alternate version, same content as the other) 
January 24, 2022 
Hirosi Ooguri (Cal Tech/Kavli IPMU)Symmetry in QFT and GravityAbstract: I will review aspects of symmetry in quantum field theory and combine them with the AdS/CFT correspondence to derive constraints on symmetry in quantum gravity. The quantum gravity constraints to be discussed include the nogo theorem on global symmetry, the completeness of gauge charges, and the decomposition of high energy states into gauge group representations.
Video of lecture OR Video of lecture (alternate version, same content as the other)

April 13, 2020 
Edward Witten (IAS)Volumes and Random MatricesAbstract: I will describe recent results relating twodimensional gravity and supergravity; volumes of moduli spaces of Riemann surfaces and super Riemann surfaces; and random matrix ensembles. See https://arxiv.org/abs/1903.11115 by Saad, Shenker, and Stanford; https://arxiv.org/abs/1907.03363 by Stanford and me. 
April 27, 2020 
Kevin Costello (Perimeter Institute)Topological strings, twistors, and SkyrmionsAbstract: It has long been known that holomorphic field theories on twistor space lead to "physical" field theories on Minkowski space. In this talk I will discuss a type I (unoriented) version of the topological B model on twistor space. The corresponding theory on Minkowski space is a sigmamodel with target the group SO(8). This is a variant of the Skyrme model that appears as the lowenergy effective theory of mesons in QCD. (The group SO(8) appears because of the GreenSchwarz mechanism in the topological string). The origin of this model in the topological string implies many remarkable properties. For one thing, the model is, in a certain sense, integrable. Further, although the Lagrangian is powercounting nonrenormalizable, counterterms at all loops can be uniquely fixed. 
May 11, 2020 
Mark Gross (Cambridge)Intrinsic Mirror SymmetryAbstract: I will talk about joint work with Bernd Siebert, proposing a general mirror construction for log CalabiYau pairs, i.e., a pair (X,D) with D a "maximally degenerate" boundary divisor and K_X+D=0, and for maximally unipotent degenerations of CalabiYau manifolds. We accomplish this by constructing the coordinate ring or homogeneous coordinate ring respectively in the two cases, using certain kinds of GromovWitten invariants we call "punctured invariants", developed jointly with Abramovich and Chen. 
May 18, 2020 
Miranda Cheng (Univ. of Amsterdam/National Taiwan University)Quantum Modularity from 3ManifoldsAbstract: Quantum modular forms are functions on rational numbers that have rather mysterious weak modular properties. Mock modular forms and false theta functions are examples of holomorphic functions on the upperhalf plane which lead to quantum modular forms. Inspired by the 3d3d correspondence in string theory, a new topological invariants named homological blocks for (in particular plumbed) threemanifolds have been proposed a few years ago. My talk aims to explain the recent observations on the quantum modular properties of the homological blocks, as well as the relation to logarithmic vertex algebras. The talk will be based on a series of work in collaboration with Sungbong Chun, Boris Feigin, Francesca Ferrari, Sergei Gukov, Sarah Harrison, and Gabriele Sgroi. 
June 1, 2020 
Davide Gaiotto (Perimeter Institute)Integrable Kondo problems and affine Geometric LanglandsAbstract: I will present some work on integrable line defects in WZW models and their relation to 4d CS theory, the IM/ODe correspondence and affine generalizations of Geometric Langlands constructions. 
June 15, 2020 
Maxim Kontsevich (IHES)Spacetime analyticity in QFTAbstact: I will talk on a joint work with Graeme Segal. We propose a new axiomatics for unitary quantum field theory which includes both Lorentzian and Euclidean signatures for curved spacetime manifolds. The key to the definition is certain open domain in the space of complexvalued symmetric bilinear forms on a real vector space. The justification comes from holomorphic convexity (lower bound) and from higher gauge theories (upper bound). 
June 22, 2020 
Anton Kapustin (Cal Tech)From gapped phases of matter to Topological Quantum Field Theory and back againAbstract: I will review the connection between gapped phases of matter and Topological Quantum Field Theory (TQFT). Conjecturally, this connection becomes 11 correspondence if one restricts to a special class of phases and TQFTs (namely, invertible ones). A related conjecture is that the space of all lattice Hamiltonians describing ShortRange Entangled phases of matter is an infinite loop space. These conjectures predict that the space of lattice Hamiltonians has nontrivial cohomology in particular dimensions. We test this by constructing closed differential forms on the space of gapped lattice Hamiltonians following a suggestion by Kitaev. These differential forms can be regarded as a highercategorical generalization of the curvature of the Berry connection and correspond to WessZuminoWitten forms in field theory. 
June 29, 2020 
No meeting due to Strings 2020

July 6, 2020 
Nima ArkaniHamed (IAS)Spacetime, Quantum Mechanics and Clusterhedra at InfinityAbstract: Elementary particle scattering is perhaps the most basic physical process in Nature. The data specifying the scattering process defines a "kinematic space", associated with the onshell propagation of particles out to infinity. By contrast the usual approach to computing scattering amplitudes, involving path integrals and Feynman diagrams, invokes auxilliary structures beyond this kinematic spacelocal interactions in the interior of spacetime, and unitary evolution in Hilbert space. This description makes spacetime locality and quantummechanical unitarity manifest, but hides the extraordinary simplicity and infinite hidden symmetries of the amplitude that have been uncovered over the past thirty years. The past decade has seen the emergence of a new picture, where scattering amplitudes are seen as the answer to an entirely different sort of mathematical question involving "positive geometries" directly in the kinematic space, making surprising connections to total positivity, combinatorics and geometry of the grassmannian, and cluster algebras. The hidden symmetries of amplitudes are made manifest in this way, while locality and unitarity are seen as derivative notions, arising from the "factorizing" boundary structure of the positive geometries. This was first see in the story of "amplituhedra" and scattering amplitudes in planar N=4 SYM theory. In the past few years, a similar structure has been seen for nonsuperysmmetric "biadjoint" scalar theories with cubic interactions, in any number of dimensions. The positive geometries through to oneloop order are given by "cluster polytopes"generalized associahedra for finitetype cluster algebraswith a simple description involving "dynamical evolution" in the kinematic space. Extending these ideas involves understanding cluster algebras associated with triangulations of general Riemann surfaces. These cluster algebras are infinite, reflecting the infinite action of mapping class group. One of the manifestations of this infinity is that the "gvector fan" of the cluster algebra is not spacefilling, making it impossible to define cluster polytopes, and obstructing the connection with positive geometries and scattering amplitudes. Remarkably, incorporating noncluster variables, associated with closed loops in the Riemann surfaces, suggests a natural way of modding out by the mapping class group, canonically compactifying the cluster complex, and associating it with "clusterhedron" polytopes. Clusterhedra are conjectured to exist for all surfaces, providing the positive geometry in kinematic space for scattering amplitudes in the biadjoint scalar theory to all loop orders and all orders in the 1/N expansion. In this talk I will give a simple, selfcontained overview of this set of ideas, assuming no prior knowledge of scattering amplitudes or cluster algebras.

July 13, 2020 
Mina Aganagic (UC Berkeley)Knot categorification from mirror symmetry, via string theoryAbstract: I will describe two approaches to categorifying quantum link invariants which work uniformly for all simple Lie algebras, and originate from geometry and string theory. A key aspect of both approaches is that it is manifest that decategorification gives the quantum link invariants one set out to categorify. Many ingredients that go into the story have been found by mathematicians earlier, but string theory spells out how they should be put together for a uniform framework for knot categorification. The first approach is based on derived categories of coherent sheaves on resolutions of slices in affine Grassmannians. Some elements of it have been discovered by mathematicians earlier and others are new. The second approach is perhaps more surprising. It uses symplectic geometry and is related to the first by two dimensional (equivariant) mirror symmetry. Unlike previous symplectic geometry based approaches, it produces a bigraded homology theory. In both cases, mirror symmetry, and techniques developed to understand it play a crucial role. I will explain the string theory origin of the two approaches, and the relation to another string theory based approach, due to Witten. 
July 20, 2020 
Greg Moore (Rutgers)Breaking News About, Topologically Twisted Rank One N=2* Supersymmetric YangMills Theory On FourManifolds, Without SpinAbstract: I will report on work in progress with Jan Manschot. We generalize previous results concerning a topological theory in four dimension that generalizes both the Donaldson invariants and the VafaWitten invariants. In contrast with previous studies we include an arbitrary background spinc structure with connection. The Coulomb branch measure involves nonholomorphic topological couplings to the background spinc connection. (This violates some folklore). Using some novel identities for the $N=2*$ prepotential, the Coulomb branch integral can be evaluated explicitly using the theory of mock modular and Jacobi forms. For $b_2^+>1$ the path integral can be written explicitly in terms of SeibergWitten invariants and modular functions of the ultraviolet coupling. We discuss the orbit of partition functions of the three rank one $N=2*$ theories under the action of Sduality. Video of Lecture 
July 27, 2020 
No meeting due to StringMath 2020

August 3, 2020 
Sakura SchaferNameki (Oxford)5d SCFTs: Symmetries and Moduli SpacesAbstract: I will report on recent developments in 5d SCFTs, studying their global symmetries, 0 and higherform, Mtheory on a canonical singularity. We provide a geometric characterization of the Coulomb and Higgs branch moduli spaces and connect this to recent work on magnetic quivers in 3d. 
August 10, 2020 
Ben Webster (Waterloo)3d mirror symmetry and its discontentsAbstract: One of the central topics of the interaction between QFT and math is mirror symmetry for 2d theories. This theory has a more mysterious and exotic friend one dimension higher, sometimes called 3d mirror symmetry, which relates two 3dimensional theories with N=4 supersymmetry. For roughly a decade, I struggled to understand this phenomenon without understanding what most of the words in the previous sentence meant. Eventually, I wised up and based on work of Braverman, Finkelberg, Nakajima, Dimofte, Gaiotto, Hilburn and others, I actually did learn a little bit, and will now try to explain to you what I learned. This knowledge has some interesting payoffs in the mathematics related to 3d theories, such as an understanding of Bezrukavnikov and Kaledin's noncommutative resolutions of the Coulomb branch, and explaining a lot of interesting Koszul dualities between category O's. 
August 17, 2020 
Marco Gualtieri (Univ. of Toronto)Branes in symplectic groupoidsAbstract: After reviewing coisotropic Abranes in symplectic manifolds and their role in mirror symmetry and geometric quantization, I will explain how the problem of holomorphic quantization of Poisson brackets may be recast, and in some cases solved, as a problem of computing morphisms between coisotropic branes in symplectic groupoids. This is joint work with Francis Bischoff and Joshua Lackman. 
August 24, 2020 
Laura Fredrickson (Stanford/U. Oregon)The asymptotic geometry of the Hitchin moduli spaceAbstract: Hitchin's equations are a system of gauge theoretic equations on a Riemann surface that are of interest in many areas including representation theory, Teichmuller theory, and the geometric Langlands correspondence. The Hitchin moduli space carries a natural hyperkahler metric. An intricate conjectural description of its asymptotic structure appears in the work of physicists GaiottoMooreNeitzke and there has been a lot of progress on this recently. I will discuss some recent results using tools coming out of geometric analysis which are wellsuited for verifying these extremely delicate conjectures. This strategy often stretches the limits of what can currently be done via geometric analysis, and simultaneously leads to new insights into these conjectures. 
September 14, 2020 
David Jordan (Edinburgh)Quantum geometric Langlands as a fully extended TFTI will survey several recent works realizing Betti geometric Langlands and its quantization as fully extended TFT's. In physics terms this is most closely related to the KapustinWitten twist of N=4 d=4 SYM at generic values of \Psi. I will outline numerous applications to quantum topology, most notably to a conjecture of Witten on finitedimensionality of skein modules, a conjecture of BonahonWong concerning skein modules at rootofunity parameters, a proposal of BenZvi concerning cluster varieties and factorization homology, and an appearance of the typeA spherical DAHA from a oncemarked torus. Finally, I will present a novel conjectural appearance of Sduality in the study of skein modules of 3manifolds. 
September 21, 2020 
Lauren Williams (Harvard)How is the hypersimplex related to the amplituhedron?Abstract: In 1987, GelfandGoreskyMacPhersonSerganova made a beautiful connection between the geometry of the Grassmannian and convex polytopes, via the moment map; the moment map image of the Grassmannian Gr(k,n) is a polytope known as the hypersimplex Delta(k,n). In 2013, motivated by the desire to give a geometric basis for the computation of scattering amplitudes in N=4 SYM, ArkaniHamed and Trnka introduced the amplituhedron A(n,k,m) as the image of the positive Grassmannian Gr+(k,n) under a linear map Z from R^n to R^{k+m} which is totally positive. While the case m=4 is most relevant to physics, the amplituhedron makes sense for any m. In my talk I will explain some strange parallels between the positroidal subdivisions of the hypersimplex Delta(k+1,n) and the m=2 amplituhedron A(n,k,2). One link is provided by the positive tropical Grassmannian. Attributions: based on joint works with Tomek Lukowski, Matteo Parisi, and David Speyer. Disclaimer: I'm neither a geometer nor a physicist. 
October 5, 2020 
Natalie Paquette (IAS)BorcherdsKacMoody algebras, 2d strings, & other curiositiesAbstract: In this talk we will extol the virtues of compactifying critical string theory down to few noncompact spacetime dimensions (particularly two). These string vacua possess rich groups of dualities. BPSsaturated quantities, which mathematically are described by automorphic forms, are invariant under such duality transformations. Further, such BPS states can furnish representations of interesting algebras, such as infinitedimensional Lie algebras. In this talk, we explore some particularly nice, concrete examples, which employ holomorphic super vertex operator algebras in our `compactification' theories. The BPS states in these models organize into representations of algebras, which we prove are (new) examples of BorcherdsKacMoody superalgebras. Video of Lecture 
October 19, 2020 
Djordje Radicevic (Brandeis)The LatticeContinuum Correspondence in Quantum MechanicsAbstract: It is very well known that longdistance correlation functions of many lattice systems can be calculated from continuum QFTs. Making this correspondence more precise  identifying continuum operators that correspond to individual lattice operators, or exhibiting the lattice origins of subtler continuum phenomena like operator product expansions  has proven quite daunting. In this talk, I will report on recent progress in this direction, using quantum mechanics (QFT in 0+1 dimensions) as an example. I will show how a finite but large quantum system can be systematically reduced to an Ersatz continuum theory, using both Hamiltonian and path integral formalisms. Along the way I will point out the lattice origins of several familiar continuum concepts, including contact terms, scale invariance, and the distinction between compact and noncompact theories. I will also stress the limitations imposed on the emergent continuum theory by its lattice progenitor  for instance, any supersymmetric continuum theory emerging from a finite theory must have a vanishing Witten index. Video of Lecture 
November 2, 2020 
Christopher Beem (Oxford)HallLittlewood Chiral Rings and Derived Higgs BranchesAbstract: I will discuss a relatively novel algebraic structure arising in fourdimensional N=2 superconformal field theories: the HallLittlewood Chiral Ring (HLCR). The HLCR is an enhancement of the more familiar Higgs branch chiral ring (which encodes the Higgs branch of the moduli space of vacua as an algebraic variety). The HLCR in gauge theories is constructed as the cohomology of a kind of BRST complex, which allows it to be identified with the ring of functions on the derived Higgs branch (in the sense of derived algebraic geometry). I will describe the solution of the HLCR cohomology problem for a large class of Lagrangian theories (the class S theories of type A1), which illustrate some interesting phenomena. This talk is based on work in progress with Diego Berdeja Suárez. Video of Lecture 
November 16, 2020 
Sergei Gukov (Cal Tech)Rokhlin, quantum groups, and BPS statesAbstract: What do ADO polynomials, cobordism invariants, and affine Grassmannians have in common? We will discuss how these seemingly different objects can be put under one roof of a BPS qseries that, on the one hand, can be thought of as a 3d analogue of the VafaWitten partition function and, on the other hand, is associated to quantum groups at generic q where Verma modules with arbitrary complex weights play an important role. Video of Lecture 
November 30, 2020 
Sourav Chatterjee (Stanford)Strong mass gap implies quark confinementAbstract: I will show that if a lattice gauge theory has exponential decay of correlations under arbitrary boundary conditions (which I call strong mass gap), and the gauge group has a nontrivial center, then Wilson's area law holds. 
December 14, 2020 
Harold Williams (USC)Canonical Bases for Coulomb BranchesAbstract: Following work of KapustinSaulina and GaiottoMooreNeitzke, one expects halfBPS line defects in a 4d N=2 field theory to form a monoidal category with a rich structure. In general, a mathematical definition of this category is not known. In this talk we discuss an algebrogeometric proposal in the case of gauge theories with polarizable matter. The proposed category is the heart of a nonstandard tstructure on the dg category of coherent sheaves on the derived BravermanFinkelbergNakajima space of triples. We refer to its objects as Koszulperverse coherent sheaves, as this tstructure interpolates between the perverse coherent tstructure and certain tstructures appearing in the theory of Koszul duality (specializing to these in the case of a pure gauge theory and an abelian gauge theory, respectively). As a byproduct, this defines a canonical basis in the associated quantized Coulomb branch by passing to classes of irreducible objects. This is joint work with Sabin Cautis. Video of Lecture 