Below is a list of Mathematical Physics Seminars held prior to the current academic year. For information on the current academic year’s seminars, please click here.
Date  Speaker  Title/Abstract 

9/9/2019  Daniel Pomerleano (UMass Boston)  Title: Intrinsic mirror symmetry via symplectic topology
Abstract: Given a maximally degenerate log Calabi–Yau variety $X$, I will describe how one can recover the birational class of the mirror manifold from a Floer theoretic invariant of $X$ (symplectic cohomology). I will then explain how this result relates to recent constructions in mirror symmetry due to Gross–Hacking–Keel and Gross–Siebert. 
9/16/2019  Eirik Eik Svanes (King’s College London and ICTP)  Title: On coupled moduli problems and effective topological theories
Abstract: I will discuss recent developments in understanding coupled moduli spaces for geometries which appear naturally in string theory. Focusing on heterotic geometries and $SU(3)$ and $G2$ structure compactifications in particular, which also come equipped with a gauge sector, I will describe how the moduli are captured by effective quasitopological theories derived from the heterotic supergravity. In the case of $SU(3)$ structure compactifications the topological theory in question is a natural generalization of holomorphic Chern–Simons theory or Donaldson–Thomas theory. In the case of heterotic $G2$ structures we will see that the moduli problem is a lot more coupled, and the moduli space has no intrinsic fibration structure in general. 
9/25/2019 Wednesday 
Fenglong You (University of Alberta)  Title: Gluing Periods for DHT Mirrors
Abstract: Let $X$ be a Calabi–Yau manifold that admits a Tyurin degeneration to a union of two quasiFano varieties $X_1$ and $X_2$ intersecting along a smooth anticanonical divisor $D$. Doran–Harder–Thompson conjectured that the Landau–Ginzburg mirrors of $(X_1,D)$ and $(X_2,D)$ can be glued to obtain the mirror of $X$. In this talk, I will explain how periods on the mirrors of $(X_1,D)$ and $(X_2,D)$ are related to periods on the mirror of $X$. The relation among periods relates different Gromov–Witten invariants via their respective mirror maps. This is joint work with Charles Doran and Jordan Kostiuk. 
9/30/2019  Dmitry Tonkonog (Harvard)  Title: Floer theory and rigid subsets of symplectic manifolds
Abstract: Suppose we are given a symplectic manifold. What general things can we say about the dynamics of its symplectomorphisms? A classical way to explore this question is to find rigid subsets: subsets that cannot be displaced from themselves by any symplectomorphism. This has inspired many developments in Floer theory, including recent ones. I will survey the topic, and prove that Lagrangian skeleta of divisor complements of Calabi–Yau manifolds are rigid. This partially reports on joint work with Umut Varolgunes, as well as other things I learned from him. 
10/7/2019  Xiao Zheng (Boston University) 
Abstract: In this talk, I will introduce an equivariant mirror construction using a Morse model of equivariant Lagrangian Floer theory, formulated in a joint work with Kim and Lau. In case of semiFano toric manifold, our construction recovers the $T$equivariant Landau–Ginzburg mirror found by Givental. For toric Calabi–Yau manifold, the equivariant disc potentials of certain immersed Lagrangians are closely related to the open Gromov–Witten invaraints of Aganagic–Vafa branes, which were studied by Katz–Liu, Graber–Zaslow, Fang–Liu–Zong and many others using localization techniques. The later result is a work in progress joint with Hong, Kim and Lau.

10/14/2019  Columbus Day  
10/21/2019
12:10pm 
ManWai Cheung (Harvard)  Title: Compactification for cluster varieties without frozen variables of finite type
Abstract: Cluster varieties are blow up of toric varieties. They come in pairs $(A,X)$, with $A$ and $X$ built from dual tori. Compactifications of $A$, studied by Gross, Hacking, Keel, and Kontsevich, generalize the polytope construction of toric varieties while the compactifications of X, studied by Fock and Goncharov, generalize the fan construction. The conjecture is that the $A$ and the $X$ cluster varieties are mirrors to each other. Together with Tim Magee, we have shown that there exists a positive polytope for the type $A$ cluster varieties which give us a hint to the Batyrev–Borisov construction. 
10/28/2019
G02 
Max Zimet
(BHI) 
Title: K3 metrics from little string theory
Abstract: Calabi–Yau manifolds have played a central role in both string theory and mathematics for decades, but in spite of this no Ricciflat metric on a compact nontoroidal Calabi–Yau manifold is known. I will discuss a new physically motivated approach toward the determination of such metrics for K3 surfaces. The key remaining step is the determination of a BPS spectrum of a heterotic little string theory on $T^2$. I will use string dualities to provide a number of mathematical reformulations of this problem, ranging from open string reduced Gromov–Witten theory for the mirror K3 surface (in accordance with the SYZ conjecture) to Donaldson–Thomas theory for auxiliary Calabi–Yau threefolds. Finally, I will discuss new approximations to K3 metrics near the semiflat limit that require only a minimal knowledge of this BPS spectrum. 
11/4/2019  Elana Kalashnikov (Harvard) 
Abstract: I will discuss joint work with Chiodo investigating the mirror symmetry of Calabi–Yau hypersurfaces in weighted projective spaces. I will show how given such a hypersurface endowed with a finite order automorphism of a specific type, the traditional cohomological mirror statement can be both specialised and broadened to take into account the weights of the action of the automorphism and the cohomology of its fixed locus. The main tool is Berglund–Hubsch–Krawitz duality. When the automorphism is an involution, this allows us to construct generalisations of Borcea–Voisin orbifolds in any dimension and with any number of factors (joint work with Chiodo and Veniani). For odd prime order automorphisms and dimension 2 orbifolds, this implies mirror symmetry for the associated lattice polarised K3 surfaces.

11/13/2019  Cancelled  
11/18/2019  Lampros Lamprou (MIT)  Title: Holographic order from modular chaos
Abstract: What quantum mechanical principle underlies the emergence of the local geometric structure of the holographic Universe? I will develop a notion of chaos associated to the entanglement pattern of a QFT state by introducing a bound characterizing modular flow of a subregion. In AdS/CFT, saturation of modular chaos is intimately linked to the local Poincare symmetry and curvature about a bulk RyuTakayanagi surface, suggesting an appealing candidate answer to the question posed above. 
11/25/2019  Time: 12:00 – 1:00pm
Speaker: David Svoboda (Perimeter Institute) Title: From paraHermitian geometry to mirror symmetry Abstract: In recent years, paraHermitian geometry has been used to describe Tduality covariant spacetimes for string theory. In my talk, I will present applications of paraHermitian geometry to 2D (2,2) SUSY sigma models and show that this geometry gives rise to a new, yet unexplored, notion of mirror symmetry. Time: 3:00 – 4:00pm Speaker: Philsang Yoo (Yale) Title: From Quantum Field Theory to Geometric Representation Theory Abstract: Quantum Field Theory is a framework of fundamental physics, which in particular has played important roles in the modern development of various subjects in mathematics, including enumerative geometry, knot theory, and lowdimensional topology. On the other hand, Geometric Representation Theory is a subject in mathematics that studies a linear model of various types of symmetries using powerful techniques of algebraic geometry. In recent years, there has been much progress relating the two subjects, enriching the subject of Geometric Representation Theory. In this colloquium style talk, we will review some recent advancements on the topic. No prior knowledge of either Quantum Field Theory or Geometric Representation Theory will be assumed. 

12/2/2019 
W. A. ZunigaGalindo (CINVESTAV)  Title: Strings and Quantum Fields Over pAdic Spacetimes
Abstract: I will discuss some recent results on the connections between local zeta functions with the regularization of padic KobaNielsen string amplitudes, and with the construction of quantum fields over padic spacetimes. The theory of local zeta functions was started in the 50s by Gel’fand and Weil. In the 70s Igusa developed a uniform theory of local zeta functions over local fields of characteristic zero. In the last years the theory has suffered a tremendous expansion due to the introduction of the motivic Igusa zeta functions by Denef and Loeser. By using the theory of local zeta functions is possible to establish (in rigorous way) the regularization of KobaNielsen amplitudes on R, C or Q_{p}. There is empirical evidence that in the limit p approaches to one, the padic strings are related with the ordinary ones. The theory of local zeta functions allows to define rigorously the limit p tends to one of padic KobaNielsen amplitudes. Since the 50s is known that the existence of fundamental solutions (Green functions) is consequence of the existence of meromorphic continuation for the Archimedean local zeta functions. This fact is also true in the padic case, for this reason the padic local zeta functions play a central role in the construction of quantum fields over padic spacetimes. 
12/9/2019  Jieqiang Wu (MIT)  Title: Covariant phase space with boundaries
Abstract: The covariant phase space method of Iyer, Lee, Wald, and Zoupas gives an elegant way to understand the Hamiltonian dynamics of Lagrangian ﬁeld theories without breaking covariance. However, in the original literature, the authors didn’t systematically treat the total derivatives and boundary terms. In this talk, I will introduce a systematic treatment of the covariant phase space formalism for ﬁeld theories with spatial boundaries. With this formalism, we can give an explicit algorithm for the Hamiltonian, only assuming that the configurations satisfy the equations of motion and boundary conditions. Our formalism also produce an extra boundary term in the Hamiltonian, which is non zero even in Einstein’s general relativity with permissive gauge fixing at the boundary. To illustrate this covariant phase space formalism, we study an interesting example the JackiwTeitelboim gravity, where we can explicitly solve the phase space and symplectic form. Reference: arXiv:1906.08616 
Date  Speaker  Title/Abstract 
9/10/2018  Xiaomeng Xu, MIT  Title: Stokes phenomenon, YangBaxter equations and GromovWitten theory.
Abstract: This talk will include a general introduction to a linear differential system with singularities, and its relation with symplectic geometry, YangBaxter equations, quantum groups and 2d topological field theories. 
9/17/2018  Gaetan Borot, Max Planck Institute  Title: A generalization of Mirzakhani’s identity, and geometric recursion
Abstract: McShane obtained in 1991 an identity expressing the function 1 on the Teichmueller space of the oncepunctured torus as a sum over simple closed curves. It was generalized to bordered surfaces of all topologies by Mirzakhani in 2005, from which she deduced a topological recursion for the WeilPetersson volumes. I will present new identities which represent linear statistics of the simple length spectrum as a sum over homotopy class of pairs of pants in a hyperbolic surface, from which one can deduce a topological recursion for their average over the moduli space. This is an example of application of a geometric recursion developed with Andersen and Orantin. 
9/24/2018  Yi Xie, Simons Center  Title: sl(3) Khovanov module and the detection of planar thetagraph
Abstract: In this talk we will show that Khovanov’s sl(3) link homology together with its module structure can be generalized for spatial webs (bipartite trivalent graphs).We will also introduce a variant called pointed sl(3) Khovanov homology. Those two combinatorial invariants are related to KronheimerMrowka’s instanton invariants $J^\sharp$ and $I^\sharp$ for spatial webs by two spectral sequences. As an application, we will prove that sl(3) Khovanov module and pointed sl(3) Khovanov homology both detect the planar theta graph. 
10/01/2018  Dori Bejleri, MIT  Title: Stable pair compactifications of the moduli space of degree one del Pezzo surfaces via elliptic fibrations
Abstract: A degree one del Pezzo surface is the blowup of P^2 at 8 general points. By the classical CayleyBacharach Theorem, there is a unique 9th point whose blowup produces a rational elliptic surface with a section. Via this relationship, we can construct a stable pair compactification of the moduli space of anticanonically polarized degree one del Pezzo surfaces. The KSBA theory of stable pairs (X,D) is the natural extension to dimension 2 of the DeligneMumfordKnudsen theory of stable curves. I will discuss the construction of the space of interest as a limit of a space of weighted stable elliptic surface pairs and explain how it relates to some previous compactifications of the space of degree one del Pezzo surfaces. This is joint work with Kenny Ascher. 
10/08/2018  PeiKen Hung, MIT  Title: The linear stability of the Schwarzschild spacetime in the harmonic gauge: odd part
Abstract: We study the odd solution of the linearlized Einstein equation on the Schwarzschild background and in the harmonic gauge. With the aid of ReggeWheeler quantities, we are able to estimate the odd part of Lichnerowicz d’Alembertian equation. In particular, we prove the solution decays at rate $\tau^{1+\delta}$ to a linearlized Kerr solution. 
10/15/2018  Chris Gerig, Harvard  Title: A geometric interpretation of the SeibergWitten invariants
Abstract: Whenever the SeibergWitten (SW) invariants of a 4manifold X are defined, there exist certain 2forms on X which are symplectic away from some circles. When there are no circles, i.e. X is symplectic, Taubes’ “SW=Gr” theorem asserts that the SW invariants are equal to welldefined counts of Jholomorphic curves (Taubes’ Gromov invariants). In this talk I will describe an extension of Taubes’ theorem to nonsymplectic X: there are welldefined counts of Jholomorphic curves in the complement of these circles, which recover the SW invariants. This “Gromov invariant” interpretation was originally conjectured by Taubes in 1995. This talk will involve contact forms and spinc structures. 
10/22/2018
*Room G02* 
Sze Ning Mak, Brown  Title: Tetrahedral geometry in holoraumy spaces of 4D, $\mathcal{N}=1$ and $\mathcal{N}=2$ minimal supermultiplets
Abstract: In this talk, I will review the supersymmetry algebra. For Lie algebras, the concepts of weights and roots play an important role in the classification of representations. The lack of linear “eigenequations” in supersymmetry leads to the failure to realize the JordanChevalley decomposition of ordinary Lie algebras on the supersymmetry algebra. Therefore, we introduce the concept “holoraumy” for the 4D, $\mathcal{N}$extended supersymmetry algebras, which allows us to explore the possible representations of supersymmetric systems of a specified size. The coefficients of the holoraumy tensors for different representations of the same size form a lattice space. For 4D, $\mathcal{N}=1$ minimal supermultiplets (4 bosons + 4 fermions), a tetrahedron is found in a 3D subspace of the 4D lattice parameter space. For 4D, $\mathcal{N}=2$ minimal supermultiplets (8 bosons + 8 fermions), 4 tetrahedrons are found in 4 different 3D subspaces of a 16D lattice parameter space. 
10/29/2018  Francois Greer, Simons Center  Title: Rigid Varieties with Lagrangian Spheres
Abstract: Let X be a smooth complex projective variety with its induced Kahler structure. If X admits an algebraic degeneration to a nodal variety, then X contains a Lagrangian sphere as the vanishing cycle. Donaldson asked whether the converse holds. We answer this question in the negative by constructing rigid complex threefolds with Lagrangian spheres using Teichmuller curves in genus 2. 
11/05/2018  Siqi He, Simons Center  Title: The KapustinWitten Equations, Opers and Khovanov Homology
Abstract: We will discuss a Witten’s gauge theory program to define Jones polynomial and Khovanov homology for knots inside of general 3manifolds by counting singular solutions to the KapustinWitten or HaydysWitten equations. We will prove that the dimension reduction of the solutions moduli space to the KapustinWitten equations can be identified with BeilinsonDrinfeld Opers moduli space. We will also discuss the relationship between the Opers and a symplectic geometry approach to define the Khovanov homology for 3manifolds. This is joint work with Rafe Mazzeo. 
11/12/2018  No Seminar  
11/19/2018  Yusuf Barış Kartal, MIT  Title: Distinguishing symplectic fillings using dynamics of Fukaya categories
Abstract: The purpose of this talk is to produce examples of symplectic fillings that cannot be distinguished by the dynamical invariants at a geometric level, but that can be distinguished by the dynamics and deformation theory of (wrapped) Fukaya categories. More precisely, given a Weinstein domain $M$ and a compactly supported symplectomorphism $\phi$, one can produce another Weinstein domain $T_\phi$\textbf{the open symplectic maping torus}. Its contact boundary is independent of $\phi$ and it is the same as the boundary of $T_0\times M$, where $T_0$ is the once punctured torus. We will outline a method to distinguish $T_\phi$ from $T_0\times M$. This will involve the construction of a mirror symmetry inspired algebrogeometric model related to Tate curve for the Fukaya category of $T_\phi$ and exploitation of dynamics on these models to distinguish them. 
11/26/2018  Charles Doran (fillin)Andreas Malmendier, Utah State (originally)  Speaker: Charles Doran
Title: Feynman Amplitudes from CalabiYau Fibrations Abstract: This talk is a lastminute replacement for the originally scheduled seminar by Andreas Malmendier. After briefly reviewing the interpretation of Feynman amplitudes as periods of graph hypersurfaces, we will focus on a class of graphs called the nloop sunset (or banana) graphs. For these graphs, the underlying geometry consists of very special families of (n1)dimensional CalabiYau hypersurfaces of degree n+1 in projective nspace. We will present a reformulation using fibrations induced from toric geometry, which implies a simple, iterative construction of the corresponding Feynman integrals to all loop orders. We will then reinterpret the massparameter dependence in the case of the 3loop sunset in terms of moduli of latticepolarized elliptic fibered K3 surfaces, and describe a method to construct their PicardFuchs equations. (As it turns out, the 3loop sunset K3 surfaces are all specializations of those constructed by ClingherMalmendier in the originally scheduled talk!) This is joint work with Andrey Novoseltsev and Pierre Vanhove ————— Speaker: Andreas Malmendier Title: (1,2) polarized Kummer surfaces and the CHL string Abstract: A smooth K3 surface obtained as the blowup of the quotient of a fourtorus by the involution automorphism at all 16 fixed points is called a Kummer surface. Kummer surface need not be algebraic, just as the original torus need not be. However, algebraic Kummer surfaces obtained from abelian varieties provide a fascinating arena for string compactification as they are not trivial spaces but are sufficiently simple for one to be able to analyze most of their properties in detail. In this talk, we give an explicit description for the relation between algebraic Kummer surfaces of Jacobians of genustwo curves with principal polarization and those associated to (1, 2)polarized abelian surfaces from three different angles: the point of view of 1) the binational geometry of quartic surfaces in P^3 using eveneights, 2) elliptic fibrations on K3 surfaces of Picardrank 17 over P^1 using Nikulin involutions, 3) thetafunctions of genustwo using twoisogeny. Finally, we will explain how these (1,2)polarized Kummer surfaces naturally appear as Ftheory backgrounds for the socalled CHL string. (This is joint work with Adrian Clingher.) 
12/03/2018  Monica Pate, Harvard  Title: Gravitational Memory in Higher Dimensions
Abstract: A precise equivalence among Weinberg’s soft graviton theorem, supertranslation conservation laws and the gravitational memory effect was previously established in theories of asymptotically flat gravity in four dimensions. Moreover, this triangle of equivalence was proposed to be a universal feature of generic theories of gauge and gravity. In theories of gravity in even dimensions greater than four, I will show that there exists a universal gravitational memory effect which is precisely equivalent to the soft graviton theorem in higher dimensions and a set of conservation laws associated to infinitedimensional asymptotic symmetries. 
12/10/2018  Fenglong You, University of Alberta  Title: Relative and orbifold GromovWitten theory
Abstract: Given a smooth projective variety X and a smooth divisor D \subset X, one can study the enumerative geometry of counting curves in X with tangency conditions along D. There are two theories associated to it: relative GromovWitten invariants of (X,D) and orbifold GromovWitten invariants of the rth root stack X_{D,r}. For sufficiently large r, AbramovichCadmanWise proved that genus zero relative invariants are equal to the genus zero orbifold invariants of root stacks (with a counterexample in genus 1). We prove that higher genus orbifold GromovWitten invariants of X_{D,r} are polynomials in r and the constant terms are exactly higher genus relative GromovWitten invariants of (X,D). If time permits, I will also talk about further results in genus zero which allows us to study structures of genus zero relative GromovWitten theory. This is based on joint work with HisanHua Tseng, Honglu Fan and Longting Wu. 
1/28/2019  Per Berglund (University of New Hampshire)  Title: A Generalized Construction of CalabiYau Manifolds and Mirror Symmetry
Abstract: We extend the construction of CalabiYau manifolds to hypersurfaces in nonFano toric varieties. This provides a generalization of Batyrev’s original work, allowing us to construct new pairs of mirror manifolds. In particular, we find novel K3fibered CalabiYau manifolds, relevant for type IIA/heterotic duality in d=4, N=2, string compactifications. We also calculate the threepoint functions in the Amodel following MorrisonPlesser, and find perfect agreement with the Bmodel result using the PicardFuchs equations on the mirror manifold. 
2/4/2019  Netanel (Nati) RubinBlaier (Cambridge)  Title: Abelian cycles, and homology of symplectomorphism groups
Abstract: Based on work of KawazumiMorita, ChurchFarb, and N. Salter in the classical case of Riemann surfaces, I will describe a technique which allows one to detect some higher homology classes in the symplectic Torelli group using parametrized GromovWitten theory. As an application, we will consider the complete intersection of two quadrics in $P^5$, and produce a nontrivial lower bound for the dimension of the 2nd group homology of the symplectic Torelli group (relative to a fixed line) with rational coefficients. 
2/11/2019  Tristan Collins (MIT)  Title: Stability and Nonlinear PDE in mirror symmetry
Abstract: A longstanding problem in mirror symmetry has been to understand the relationship between the existence of solutions to certain geometric nonlinear PDES (the special Lagrangian equation, and the deformed HermitianYangMills equation) and algebraic notions of stability, mainly in the sense of Bridgeland. I will discuss progress in this direction through ideas originating in infinite dimensional GIT. This is joint work with S.T. Yau. 
2/25/2019  Hossein Movasati (IMPA)  Title: Modular vector fields
Abstract: Using the notion of infinitesimal variation of Hodge structures I will define an Rvariety which generalizes CalabiYau and abelian varieties, cubic four, seven and ten folds, etc. Then I will prove a theorem concerning the existence of certain vector fields in the moduli of enhanced Rvarieties. These are algebraic incarnation of differential equations of the generating functions of GW invariants (LianYau 1995), Ramanujan’s differential equation between Eisenstein series (Darboux 1887, Halphen 1886, Ramanujan 1911), differential equations of Siegel modular forms (Resnikoff 1970, BertrandZudilin 2005). 
3/4/2019  Zhenkun Li (MIT)  Title: Cobordism and gluing maps in sutured monopoles and applications.
Abstract: The sutured monopole Floer homology was constructed by Kronheimer and Mrowka on balanced sutured manifolds. Floer homologies on closed three manifolds are functors from oriented cobordism category to the category of modules over suitable rings. It is natural to ask whether the sutured monopole Floer homology can be viewed as a functor similarly. In the talk we will answer this question affirmatively. In order to study the above problem, we will need to use an important tool called the gluing maps. Gluing maps were constructed in the Heegaard Floer theory by Honda, Kazez and Matić , while were previously unknown in the monopole theory. In the talk we will also explain how to construct such gluing maps in monopoles and how to use them to define a minus version of knot monopole Floer homology. 
3/11/2019  Yu Pan (MIT)  Title: Augmentations and exact Lagrangian cobordisms.
Abstract: Augmentations are tightly connected to embedded exact Lagrangian fillings. However, not all the augmentations of a Legendrian knot come from embedded exact Lagrangian fillings. In this talk, we introduce immersed exact Lagrangian fillings into the picture and show that all the augmentations come from possibly immersed exact Lagrangian fillings. In this way, we realize augmentations, which is an algebraic object, fully geometrically. This is a joint work with Dan Rutherford working in progress. 
3/25/2019  Eduardo Gonzalez (UMass Boston)  Title: Stratifications in gauged GromovWitten theory.
Abstract: Let G be a reductive group and X be a smooth projective Gvariety. In classical geometric invariant theory (GIT), there are stratifications of X that can be used to understand the geometry of the GIT quotients X//G and their dependence on choices. In this talk, after introducing basic theory, I will discuss the moduli of gauged maps, their relation to the GromovWitten theory of GIT quotients X//G and work in progress regarding stratifications of the moduli space of gauged maps as well as possible applications to quantum Ktheory. This is joint work with D. HalpernLeistner, P. Solis and C. Woodward. 
4/1/2019  Athanassios S. Fokas (University of Cambridge)  Title: Asymptotics: the unified transform, a new approach to the Lindelöf Hypothesis,and the ultrarelativistic limit of the Minkowskian approximation of general relativity
Abstract: Employing standard, as well as novel techniques of asymptotics, three different problems will be discussed: (i) The computation of the large time asymptotics of initialboundary value problems via the unified transform (also known as the Fokas method, www.wikipedia.org/wiki/Fokas_method)[1]. (ii) The evaluation of the large tasymptotics to all orders of the Riemann zeta function[2], and the introduction of a new approach to the Lindelöf Hypothesis[3]. (iii) The proof that the ultra relativistic limit of the Minkowskian approximation of general relativity [4] yields a force with characteristics of the strong force, including confinement and asymptotic freedom[5]. [1] J. Lenells and A. S. Fokas. The Nonlinear Schrödinger Equation with tPeriodic Data: I. Exact Results, Proc. R. Soc. A 471, 20140925 (2015). J. Lenells and A. S. Fokas, The Nonlinear Schrödinger Equation with tPeriodic Data: II. Perturbative Results, Proc. R. Soc. A 471, 20140926 (2015). [2] A.S. Fokas and J. Lenells, On the Asymptotics to All Orders of the Riemann Zeta Function and of a TwoParameter Generalization of the Riemann Zeta Function, Mem. Amer. Math. Soc. (to appear). [3] A.S. Fokas, A Novel Approach to the Lindelof Hypothesis, Transactions of Mathematics and its Applications (to appear). [4] L. Blanchet and A.S. Fokas, Equations of Motion of SelfGravitating NBody Systems in the First PostMinkowskian Approximation, Phys. Rev. D 98, 084005 (2018). [5] A.S. Fokas, Super Relativistic Gravity has Properties Associated with the Strong Force, Eur. Phys. J. C (to appear). 
4/8/2019  Yoosik Kim (Boston University)  Title: String polytopes and GelfandCetlin polytopes
Abstract: The string polytope was introduced by Littelmann and Berenstein–Zelevinsky as a generalization of the GelfandCetlin polytope in representation theory. For a connected reductive algebraic group $G$ over $\mathbb{C}$ and a dominant integral weight $\lambda$, a choice of a reduced word of the longest element in the Weyl group of G determines a string polytope. Depending on a reduced word of the longest element in the Weyl group, combinatorially distinct string polytopes arise in general. In this talk, I will explain how to classify the string polytopes that are unimodularly equivalent to GelfandCetlin polytopes when $G = \mathrm{SL}_{n+1}(\mathbb{C})$ and $\lambda$ is a regular dominant integral weight. Also, I will explain a conjectural way obtaining SYZ mirrors respecting a cluster structure invented by Fomin–Zelevinsky. This talk is based on joint work with Yunhyung Cho, Eunjeong Lee, and KyeongDong Park. 
4/15/2019
Room G02 
Junliang Shen (MIT)  Title: Perverse sheaves in hyperKähler geometry
Abstract: I will discuss the role played by perverse sheaves in the study of topology and geometry of hyperKähler manifolds. Motivated by the P=W conjecture, we establish a connection between topology of Lagrangian fibrations and Hodge theory using perverse filtrations. Our method gives new structural results for topology of Lagrangian fibrations associated with hyperKähler varieties. If time permits, I will also discuss connections to enumerative geometry of CalabiYau 3folds. Based on joint work with Qizheng Yin. 
4/22/2019  Yang Zhou (CMSA)  Title: Quasimap wallcrossing for GIT quotients
Abstract: For a large class of GIT quotients X=W//G, CiocanFontanine–Kim–Maulik have developed the theory of epsilonstable quasimap invariants. They are conjecturally equivalent to the Gromov–Witten invariants of X via explicit wallcrossing formulae, which have been proved in many cases, including targets with good torus action and complete intersections in a product of projective spaces. In this talk, we will give a proof for all targets in all genera. The main ingredient is the construction of some moduli space with C^* action whose fixedpoint loci precisely correspond to the terms in the wallcrossing formulae. 
4/29/2019
Room G02 
Zili Zhang(University of Michigan)  Title: P=W, a strange identity for Dynkin diagrams
Abstract: Start with a compact Riemann surface X with marked points and a complex reductive group G. According to HitchinSimpson’s nonabelian Hodge theory, the pair (X,G) comes with two new complex varieties: the character variety M_B and the Higgs moduli M_D. I will present some aspects of this story and discuss an identity P=W indexed by affine Dynkin diagrams – occurring in the singular cohomology groups of M_D and M_B, where P and W dwell. Based on joint work with Junliang Shen. 
5/6/2019  Dennis Borisov (CMSA) 
Abstract: I will explain the notion of shifted symplectic structures due to Pantev, Toen, Vaquie and Vaquie, and then show that a derived scheme with a 2shifted symplectic structure can be realized as critical locus of a globally defined 1shifted potential.
Joint work with Artan Sheshmani

Date………  Speaker………….  Title/Abstract 
252018  Hyungchul Kim (Pohang University of Science and Technology)  Seiberg duality and superconformal index in 3d
Abstract: I will discuss 3d N=2 supersymmetric gauge theories with a unitary gauge group and two matter fields in the adjoint representation. The low energy spectrum of BPS states of the theory can be studied from the superconformal index. The information on the low energy spectrum including monopole operators is essential to construct a Seibergtype dual theory. Superconformal indices for a dual pair of the theories should be the same, which is a physical basis for a mathematical identity. 
2122018  Matthew Stroffregen
(MIT) 
Equivariant Khovanov Spaces
Abstract: Associated to a link L in the threesphere, LipshitzSarkar constructed a topological space, welldefined up to stable homotopy, whose homology is the (even) Khovanov homology of L. We extend this to construct an “odd Khovanov space” of L, whose homology recovers odd Khovanov homology. We also equip the odd Khovanov space with a natural involution whose fixed point set is the (even) Khovanov space of LipshitzSarkar, and show that the even Khovanov space admits its own natural involution. We outline some conjectures relating the even and odd Khovanov spaces. This is joint work with Sucharit Sarkar and Chris Scaduto. 
2262018  Jordan Keller
(Harvard) 
Linear Stability of Schwarzschild Black Holes
Abstract: The Schwarzschild black holes comprise a static, spherically symmetric family of black hole solutions to the vacuum Einstein equations. The physical relevance of such solutions is intimately related to their stability under gravitational perturbations. We present results on the linear stability of the Schwarzschild black holes, joint work with PeiKen Hung and MuTao Wang. 
352018  Shinobu Hosono (Gakushuin University)  Movable vs monodromy nilpotent cones of CalabiYau manifolds
abstract: I will show two interesting examples of mirror symmetry of CalabiYau complete intersections which have birational automorphisms of infinite order. I will first describe/observe mirror correspondences between the movable cones in birational geometry and the monodromy nilpotent cones which are defined at each boundary points (called LCSLs) in the moduli spaces and naturally glued together. In doing this, I will identify “PicardLefschetzs monodromy transformations for flopping curves” in the mirror families. If time permits, I will show one more example of CalabiYau complete intersections for which we observe similar correspondence between the birational geometry and monodromy nilpotent cones. However, in this example, we observe that the correspondence becomes complete when we include a nontoric boundary point in the mirror family. This is based on a recent paper with H. Takagi (arXiv:170 
352018  Emanuel Scheidegger
(Albert Ludwigs University of Freiburg) 
Periods and quasiperiods of modular forms and the mirror quintic at the conifold.
Abstract: We review the theory of periods of modular forms and extend it to quasiperiods. General motivic conjectures predict a relation between periods and quasiperiods of certain weight 4 Hecke eigenforms associated to hypergeometric oneparameter families of CalabiYau threefolds. We verify this prediction and discuss some of its implications. 
3192018
Room G02 
Emanuel Scheidegger
(Albert Ludwigs University of Freiburg) 
From Gauged Linear Sigma Models to LandauGinzburg orbifolds via central charge functions
Abstract: We review the categorical description of the CalabiYau/LandauGinzburg correspondence in terms of equivariant matrix factorizations in the gauged linear sigma model. We present the hemisphere partition function as a central charge function in the gauged linear sigma model. We study the relation of this function in the LG phase to the Chern character of equivariant matrix factorizations of the LG potential and generating functions of FJRW invariants. 
3262018  Yi Xie
SCGP 
Surgery, Polygons and Instanton Floer homology
Abstract: Many classical numerical invariants (including Casson invariant, Alexander polynomial and Jones polynomial) for 3manifolds or links satisfy surgery formulas relating three different 3manifolds or links. All those invariants are categorified by certain Floer homologies (or Khovanov homology) which also satisfy socalled surgery exact triangles. In this talk I will discuss the notion of “surgery exact polygons” which appears in the SU(N)instanton Floer homology theory. Roughly speaking, an “ngon” is a relation among the Floer homology groups of 3manifolds obtained by n different Dehn surgeries on a fixed knot. It generalizes the surgery exact triangle in SU(2)instanton Floer homology. If time permits, I will also talk about a homologicalmirrorsymmetrytype conjecture which motivates this work. This is joint work with Lucas Culler and Aliakbar Daemi. 
422018  CheukYu Mak
Cambridge University 
Discrete Legendre transform and tropical multiplicity from symplectic geometry
Abstract:There is a long history of enumerative invariants and related problems in mirror symmetry. One powerful approach to understand it is given by counting tropical curves with multiplicities. Tropical multiplicity formula in dimension two can be easily understood but the generalization to higher dimensions is less transparent. In this talk, we explain the relation between tropical multiplicities and the torsion of the first homology group of the associated Lagrangian submanifolds/cell complexes. It is a preparation talk for the talk “Tropically constructed Lagrangians in mirror quintic threefolds”, which explains the construction of associated Lagrangian submanifolds using degeneration of hypersurface in toric orbifold.It is a joint work with Helge Ruddat. 
492018
Room G02 
Brandon B. Meredith
EmbryRiddle Aeronautical University 
Mirror Symmetry on Toric Surfaces via Tropical Geometry
Abstract: Mirror symmetry is a curious duality, first noticed by physicists and then excitedly embraced by mathematicians, between certain manifolds and their “mirror” spaces. This talk considers mirror symmetry on toric surfaces, which are varieties with certain convenient combinatorial properties and include many wellknown surfaces. These surfaces are especially suited to being exploited by tropical geometry, which is a form of algebraic geometry over the “tropical semiring.” This talk will discuss the generalization of mirror symmetry to all toric surfaces (expanded from just the Fano case) following the GrossSiebert Program wherein singularities are added to the tropical picture in order to pull more curves into view. 
4162018  Yuan Gao
Stony Brook 
Title: On the extension of the Viterbo functor
Abstract: In this talk I will describe deformations of wrapped Fukaya categories that arise from cobordisms, using which the Viterbo restriction functor can be extended to any exact cylindrical Lagrangian submanifold. I will also discuss how this extension can be viewed from the perspective of Lagrangian correspondences. 
4232018
Room G02 
Baohua Fu
Chinese Academy of Science 
Title: Equivariant compactifications of vector groups
Abstract: In 1954, Hirzebruch raised the problem to classify smooth compactifications of vector spaces with second Betti number 1, which is known till now up to dim 3. In 1999, HassettTschinkel considered the equivariant version of this problem and obtained the classification up to dim. 3. I’ll report recent progress on this (equivariant) problem. In particular, we obtain the classification up to dimension 5. 
4302018  Dmitry Tonkonog
UC Berkeley 
Title: Geometry of symplectic flux
Abstract: Symplectic flux measures the areas of cylinders swept in the process of an isotopy of a Lagrangian submanifold. This is a classical invariant which captures quantitative aspects of symplectic manifolds. I will report on joint work with Egor Shelukhin and Renato Vianna in which we study the geometry of flux using a technique inspired by mirror symmetry. 
Date……….  Name  Title/Abstract 
090417  No Talk  
09112017  YuShen Lin
(Harvad CMSA) 
From the Decomposition of PicardLefschetz Transformation to Tropical Geometry
Abstract: PicardLefschetz transformation tells the monodromy of a fibration with “good” singular fibres. In the case of fibres are Lagrangian in a symplectic $4$manifold, there is a natural decomposition of PicardLefschetz transformation into two elementary transformations from Floer theory. The idea will help to develop the tropical geometry for some hyperKahler surfaces. 
091817  Yoosik Kim
(Boston University) 
Monotone Lagrangian tori in cotangent bundles.
Abstract: As an attempt to classify Lagrangian submanifolds and due to their importance in Floer theory, monotone Lagrangian tori have been got attention. In this talk, we provide a way producing monotone Lagrangian tori in the cotangent bundles of some manifolds including spheres or unitary groups. The construction is based on the classification of Lagrangian fibers of a certain completely integrable system on a partial flag manifolds of various types. We then discuss when their Floer cohomologies (under a certain deformation by nonunitary flat line bundles) do not vanish. This talk is based on joint work with Yunhyung Cho and YongGeun Oh. 
092717  YuWei Fan
(Harvard) 
WeilPetersson geometry on the space of Bridgeland stability conditions
Abstract: Inspired by mirror symmetry, we define WeilPetersson geometry on the space of Bridgeland stability conditions on a CalabiYau category. The goal is to further understand the stringy Kahler moduli space of CalabiYau manifolds. This is a joint work with A. Kanazawa and S.T. Yau. 
100417  Dingxin Zhang
(Brandeis) 
<1 part of slopes under degeneration
Abstract: For a smooth family of projective varieties over a field of characteristic p > 0, it is known that the Newton polygon of fibers goes up under specialization. In this talk, we will show that when the family acquires singular members, the less than one part of the slopes of the Newton polygon goes up under specialization. This could be viewed as a characteristic p analogue of a simple phenomenon in Hodge theory. 
101117  No Talk  
10182017  Nati Blaier
(Harvard CMSA) 
Geometry of the symplectic Torelli group
Abstract: This talk has two parts. In the first part of the talk, I will introduce the group of symplectomorphism and try to convince you that it is a very important object in symplectic topology by surveying some known structural results and drawing a comparison with the situation in the smooth and Kahler geometries as well as the world of lowdimensional topology. In the second part, I’ll discuss the symplectic Torelli group for higher dimensional symplectic manifolds, and an ongoing project to use GromovWitten theory to detect interesting elements. 
10232017
*Monday* 
Florian Beck
(Universität Hamburg) 
Hitchin systems in terms of CalabiYau threefolds.
Abstract: Integrable systems are often constructed from geometric and/or Lietheoretic data. Two important example classes are Hitchin systems and CalabiYau integrable systems. A Hitchin system is constructed from a compact Riemann surface together with a complex Lie group with mild extra conditions. In contrast, CalabiYau integrable systems are constructed from a priori purely geometric data, namely certain families of CalabiYau threefolds. Despite their different origins there is a nontrivial relation between Hitchin and CalabiYau integrable systems. More precisely, we will see in this talk that any Hitchin system for a simplyconnected or adjoint simple complex Lie group is isomorphicto a CalabiYau integrable system (away from singular fibers). 
11012017
*12:30pm1:30pm* 
Chenglong Yu
(Harvard Math) 
PicardFuchs systems of zero loci of vector bundle sections
Abstract: We propose an explicit construction for PicardFuchs systems of zero loci of vector bundle sections. When the vector bundle admits large symmetry, the system we constructed is holonomic. This is a joint work with Huang, Lian and Yau. 
11062017
*Monday* 
Pietro Benetti Genolini(Univ. of Oxford)  Topological AdS/CFT
Abstract: I will describe a holographic dual to the DonaldsonWitten topological twist of gauge theories on a Riemannian fourmanifold. Specifically, I will consider asymptotically locally hyperbolic solutions to Romans’ gauged supergravity in five dimensions with the fourmanifold as conformal boundary, and show that the renormalised supergravity action is independent of the choice of boundary metric. This is a first step in the direction of combining topological quantum field theory with the AdS/CFT correspondence. 
11132017
*Monday 12:30pm* *Room G02* 
Yusuf Baris Kartal(MIT)  Dynamical invariants of categories associated to mapping tori
Abstract: One can construct the symplectic mapping torus for a given a symplectic manifold with a symplectomorphism and use the flux invariant to distinguish the mapping tori of maps of different order. The essential argument is that the flow in a certain direction have different periods depending on the order of the symplectomorphism. In this talk, we will introduce an abstract categorical version of the mapping torus associated to an $A_\infty$ category and an autoequivalence. Then, we will construct a family of bimodules analogous to the flow and discuss how to characterize it intrinsically and how to use it to distinguish different categorical mapping tori. 
11222017  No Talk  
11292017  Amitai Zernik
(IAS) 
Computing the A∞ algebra of RP2m CP2m using open fixedpoint localization.
Abstract: I’ll explain how to compute the equivariant quantum A∞ algebra A associated with the Lagrangian embedding of RP2m in CP2m, using a new fixedpoint localization technique that takes into account contributions from all the corner strata. It turns out that A is rigid, so its structure constants are independent of all choices. When m = 1 and in the nonequivariant limit, they specialize to give Welschinger’s counts of real rational planar curves passing through some generic, conjugation invariant congurations of points in CP2m. So we get a diagrammatic expression for computing Welschinger invariants, which I’ll demonstrate with some examples.Time permitting, I’ll discuss a formal extension to higher genus which satises string and dilaton. 
12062017  Sarah Venkatesh
(Columbia) 
Closedstring mirror symmetry for subdomains
Abstract: We construct a symplectic cohomology theory for Liouville cobordisms that detects nontrivial elements of the Fukaya category. This theory is conjecturally mirror to the Jacobian ring of a LandauGinzburg superpotential on an affinoid subdomain. We illustrate this manifestation of mirror symmetry by examining cobordisms contained in negative line bundles. 
Date  Name  Title/Abstract 
013017  Yu Qiu, CUHK  Title: Spherical twists on 3CalabiYau categories of quivers with potentials from surfaces and spaces of stability conditions
Abstract: We study the 3CalabiYau category D(S) associated to a marked surface S. In the case when S is unpunctured, we show that the spherical twist group, which is a subgroup of autoequivalence group of D(S), is isomorphic to a subgroup of the mapping class group of S_Delta–the decorated version of S. In the case when S is an annulus, we prove that the space Stab of stability conditions on D(S) is contractible. We also present working progress on proving the simply connectedness of Stab for any unpunctured case and on studying Stab for the punctured case. 
020617 
Christoph Keller, Harvard School of Applied Science and Engineering

Title: Mathieu Moonshine and Symmetry Surfing 
021317  Artan Sheshmani, Aarhus University/CMSA  Title: The theory of Nested Hilbert schemes on surfaces
Abstract: In joint work with Amin Gholampour and ShingTung Yau we construct natural virtual fundamental classes for nested Hilbert schemes on a nonsingular projective surface S. This allows us to define new invariants of S that recover some of the known important cases such as Poincare invariants of D\”{urrKabanovOkonek and the stable pair invariants of KoolThomas. In the case of the nested Hilbert scheme of points, we can express these invariants in terms of integrals over the products of Hilbert scheme of points on S, and relate them to the vertex operator formulas found by CarlssonOkounkov. The virtual fundamental classes of the nested Hilbert schemes play a crucial role in the local DonaldsonThomas theory of threefolds that I will talk about, in talk 2. 
022017  Holiday — NO SEMINAR  
022717  Wenbin Yan, CMSA  Title: ArgyresDouglas Theories, Vertex Operator Algebras and Wild Hitchin Characters
Abstract: We discuss some interesting relations among 4d ArgylesDouglas (AD) theories, vertex operator algebras (VOA) and wild Hitchin system. We use the Coulomb branch index of AD theories to study geometric and topological data of moduli spaces of wild Hitchin system. These data show an one to one map between fixed points on the moduli space and irreducible modules of the VOA. Moreover, a limit of the Coulomb branch index of AD theories can be identified with matrix elements of the modular transform ST^kS in certain twodimensional VOAs. The appearance of VOAs, which was known previously to be associated with Schur operators but not Coulomb branch operators, is somewhat surprising. 
030617  Tom Rudelius, Harvard University  Title: 6D SCFTs and Group Theory
Abstract: We will explore the surprising connection between certain classes of homomorphisms and certain classes of noncompact CalabiYau manifolds using 6D superconformal field theories as an intermediate link. 
031317  Spring Break — NO SEMINAR  
032017  Philippe Sosoe, CMSA  Title: New bounds for the chemical distance in 2D critical percolation
Abstract: We consider the problem of estimating the length, in lattice spacings, of the shortest open connection between the two vertical sides of a square of side length N in critical percolation, when N tends to infinity. This is known as the chemical distance between the sides. Kesten and Zhang asked if this length is asymptotically negligible compared to the length of the ”lowest crossing”, whose length can be expressed in terms of arm exponents and thus calculated quite precisely on the hexagonal lattice. With M. Damron and J. Hanson, we answered this question in 2015. In this talk, we present improved estimates on the chemical distance, using a new iteration technique. 
032717  Agnese Bissi, Harvard University  Title: Loops in AdS from conformal symmetry
Abstract: In this talk I will discuss a new use for conformal field theory crossing equation in the context of AdS/CFT: the computation of loop amplitudes in AdS, dual to nonplanar correlators in holographic CFTs. I will revisit this problem and the dual 1/N expansion of CFTs, in two independent ways. The first is to show how to explicitly solve the crossing equations to the first subleading order in 1/N^2, given a leading order solution. This is done as a systematic expansion in inverse powers of the spin, to all orders. These expansions can be resummed, leading to the CFT data for finite values of the spin. The second approach involves Mellin space. As an example, I’ll show how the polar part of the fourpoint, looplevel Mellin amplitudes can be fully reconstructed from the leadingorder data. The anomalous dimensions computed with both methods agree. In the case of \phi^4 theory in AdS, the crossing solution reproduces a previous computation of the oneloop bubble diagram. I will end with a discussion on open problems and new developments. 
040317  Nathan Haouzi, University of California, Berkeley  Title: Little Strings and Classification of surface defects
Abstract: The socalled 6d (2,0) conformal field theory in six dimensions, labeled by an ADE Lie algebra, has become of great interest in recent years. Most notably, it gave new insights into lower dimensional supersymmetric field theories, for instance in four dimensions, after compactification. In this talk, I will talk about a deformation of this CFT, the sixdimensional (2,0) little string theory: its origin lies in type IIB string theory, compactified on an ADE singularity. We further compactify the 6d little string on a Riemann surface with punctures. The resulting defects are Dbranes that wrap the 2cycles of the singularity. This construction has many applications, and I will focus on one: I will provide the little string origin of the classification of surface defects of the 6d (2,0) CFT, for ADE Lie algebras. Furthermore, I will give the physical realization of the socalled BalaCarter labels that classify nilpotent orbits of these Lie algebras. 
041017  Burkhard Schwab, Harvard CMSA  Title: Large Gauge symmetries in Supergravity
Abstract: In the recent literature, a class of new symmetries — collectively known as “large gauge symmetries” — has emerged that governs the scattering of massless particles of very low energy on asymptotically flat space times. I will show that this statement extends to supergravity where an infinite family of fermionic symmetries can be derived. The algebra of these fermionic symmetries close in the BMS group and their Ward identity is the factorization of soft gravitinos in the Smatrix. 
041717  Ingmar Saberi, Universität Heidelberg  Title: Holographic lattice field theories
Abstract: Recent developments in tensor network models (which are, roughly speaking, quantum circuits designed to produce analogues of the ground state in a conformal field theory) have led to speculation that such networks provide a natural discretization of the AdS/CFT correspondence. This raises many questions: just to begin, is there any sort of dynamical model or lattice field theory underlying this connection? And how much of the usual AdS/CFT dictionary really makes sense in a discrete setting? I’ll describe some recent work that proposes a setting in which such questions can perhaps be addressed: a discrete spacetime whose bulk isometries nevertheless match its boundary conformal symmetries. Many of the first steps in the AdS/CFT dictionary carry over without much alteration to lattice field theories in this background, and one can even consider natural analogues of BTZ black hole geometries. 
042417  Patrick Jefferson, Harvard University  Title: Towards a classification of 5d N = 1 SCFTs
Abstract: I will discuss a new proposal for classifying fivedimensional SCFTs with N = 1 supersymmetry and a simple gauge algebra. This classification program entails studying supersymmetryprotected quantities on the Coulomb branch of moduli space using only representationtheoretic data, and subsumes all known predictions in the literature while predicting the existence of novel theories. Geometric constructions of 5d N = 1 theories via string compactifications interpret the supersymmetric protected data as geometric data associated to a local CalabiYau threefold, suggesting the possibility of translating this program into a partial cataloguing of CalabiYau geometries. 
050117  NO SEMINAR  
050817  NO SEMINAR  
051517  
052217  
052917 
Date  Name  Title/Abstract 
091216  Chong Wang, Harvard  Title: A duality web in 2+1 dimensions
Abstract: I will discuss a web of field theory dualities in 2+1 dimensions that generalize the known particle/vortex duality. Some of these dualities relate theories of fermions to theories of bosons. Others relate different theories of fermions. Assuming some of these dualities, other dualities can be derived. I will present several consistency checks of the dualities and relate them to Sdualities in 3+1 dimensions. 
091916  Johannes Kleiner, University of Regensburg  Title: A New Candidate for a Unified Physical Theory
Abstract: The CFS theory is a new approach to describe fundamental physics. Giving quantum mechanics, general relativity and quantum field theory as limiting cases, it is a candidate for a unified physical theory. The goal of my talk is to explain the basic concepts and the general physical picture behind the approach. In particular, I will focus on the connection to contemporary physics. 
092616  Can Kozcaz, CMSA 
We explore a one parameter ζdeformation of the quantummechanical SineGordon and DoubleWell potentials which we call the Double SineGordon (DSG) and the Tilted Double Well (TDW), respectively. In these systems, for positive integer values of ζ, the lowest ζ states turn out to be exactly solvable for DSG – a feature known as QuasiExactSolvability (QES) – and solvable to all orders in perturbation theory for TDW. For DSG such states do not show any instantonlike depen dence on the coupling constant, although the action has real saddles. On the other hand, although it has no real saddles, the TDW admits allorders perturbative states that are not normalizable, and hence, requires a nonperturbative energy shift. Both of these puzzles are solved by including complex saddles. 
100316 
Masahito Yamazaki, IMPU

Title: Conformal Blocks and Verma Modules abstract: (for physicists) I will discuss analytic structures of the conformal block as a function of the scaling dimension. This will lead us torecursion relations for conformal blocks, which are also efficient for numerics. (for mathematicians) I will discuss representation theory of parabolic Verma modules for basic Lie superalgebras. In particular I will introduce a new determinant formula for the contravariant form. 
101716  Fabian Haiden, Harvard 
Title: “Balanced filtrations and asymptotics for semistable objects.” I will discuss some recent results which came out of the study of the flow on metrized quiver representations. This flow is a finitedimensional toy model for nonlinear heattype flows. In joint work with Katzarkov, Kontsevich, and Pantev, we find that the asymptotics of the flow on a given quiver representation define a filtration (indexed by R^\infty) which has a purely algebraic interpretation. A novel feature is the existence of nonlinear walls, on which asymptotics of the metric are described by nested logarithms. 
102416 
Arnav Tripathy, Harvard University

Spinning BPS states and motivic DonaldsonThomas invariants I’ll describe a new chapter in the enumerative geometry of the K3 surface and its product with an elliptic curve in a long line of extensions starting from the classic YauZaslow formula for counts of rational nodal curves. In particular, I’ll give a stringtheoretic derivation of the threefold’s motivic DonaldsonThomas invariants given the Hodgeelliptic genus of the K3, a new quantity interpolating between the Hodge polynomial and the elliptic genus. 
103116 
Joseph Minahan, Uppsala University

Supersymmetric gauge theories on $d$dimensional spheres Abstract: In this talk I discuss localizing super YangMills theories on spheres in various dimensions. Our results can be continued to noninteger dimensions, at least perturbatively, and can thus be used to regulate UV divergences. I will also show how this can provide a way to localize theories with less supersymmetry. 
110716 
SeungJoo Lee, Virginia Tech

Multiple Fibrations in CalabiYau Geometry and String Dualities Abstract: We study the ubiquity of multiple fibration structures in known constructions of CalabiYau manifolds and explore the role they play for string dualities. Upon introducing new tools for resolved CalabiYau varieties, we analyze a set of Ftheory effective theories associated to the different elliptic fibrations and relate them via the M/Ftheory correspondence. Explicit geometric examples will include higherrank MordellWeil groups and nonflat fibrations. In addition, in the context of heterotic/Ftheory duality, we also investigate the role played by multiple nested structures of K3 and elliptic fibrations in known and novel string dualities in various dimensions. 
111416 
Thomas Walpuski, MIT 
Title: Singular PHYM connections (on ACyl Kähler manifolds) Abstract: The celebrated Donaldson–Uhlenbeck–Yau Theorem asserts that a holomorphic vector bundle over a compact Kähler manifolds admits a projectively Hermitian Yang–Mills (PHYM) metric if and only if it is μ–polystable. Using a geometric regularization scheme, Bando–Siu extended the DUY Theorem to reflexive sheaves; however, they leave the singularities of the PHYM metrics unstudied. In the first part of this talk I will discuss a version of the DUY/BS Theorem for asymptotically cylindrical Kähler manifolds. I will briefly explain our motivation coming from G2 gauge theory and then sketch the crucial step of proof, which is how to use μ–stability at infinity to obtain a priori C^0 estimates. The second part of this talk focuses on understanding the singularities of PHYM metrics. In particular, I will explain a simple proof of uniqueness of tangent cones for singular projectively Hermitian Yang–Mills connections on reflexive sheaves at isolated singularities modelled on μ–polystable holomorphic bundles over \P^{n1}. This is joint work with A. Jacob and H. Sá Earp. 
112116 
Hee Cheol Kim, Harvard Physics

Title: Defects and instantons in 5d SCFTs Abstract : In this talk I will discuss various BPS defects in 5d SUSY field theories. In the first part, I will talk about codimension 4 defects and their interaction with instanton particles. I will show that the partition function of this codimension 4 defect is related to Nekrasov’s qqcharacter. In the second part, I will talk about codimension 2 defects and instanton partition functions. I will also explain that the partition functions of the codimension 2 defects give rise to eigenfunctions of associated integral Hamiltonians. 
112816  NO MEETING THIS WEEK  
120516  Hansol Hong, CMSA 
Title: “Mirror construction via formal deformation of Lagrangians” Abstract: I’ll briefly review algebraic structures on categories that appear in homological mirror symmetry, and explain how the deformation of this algebraic structure on a Fukaya category can arise a mirror space. 
121216 