The seminar on mathematical physics will be held every Monday from 12 – 1pm in CMSA Building, 20 Garden Street, Room G10.
The list of speakers is below and will be updated as details are confirmed. Titles for the talks will be added as they are received.
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  
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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 