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.
2017 Fall Semester:
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 