Mathematical Physics Seminar, Mondays

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
01-30-17  Yu Qiu, CUHKScreen Shot 2017-01-03 at 4.51.23 PM Title: Spherical twists on 3-Calabi-Yau categories of quivers with potentials from surfaces and spaces of stability conditions

Abstract: We study the 3-Calabi-Yau 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 auto-equivalence 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.


Christoph Keller, Harvard School of Applied Science and Engineering


 Title: Mathieu Moonshine and Symmetry Surfing
02-13-17 Artan Sheshmani, Aarhus University/CMSA


Title: The theory of Nested Hilbert schemes on surfaces

Abstract: In joint work with Amin Gholampour and Shing-Tung 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\”{urr-Kabanov-Okonek and the stable pair invariants of Kool-Thomas. 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 Carlsson-Okounkov. The virtual fundamental classes of the nested Hilbert schemes play a crucial role in the local Donaldson-Thomas theory of threefolds that I will talk about, in talk 2.

02-20-17  Holiday — NO SEMINAR


Date Name Title/Abstract
09-12-16 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 S-dualities in 3+1 dimensions. 

09-19-16 Johannes Kleiner, University of Regensburg

Screen Shot 2016-08-30 at 11.58.35 AM

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.

09-26-16 Can Kozcaz, CMSA


Cheshire Cat Resurgence

We explore a one parameter ζ-deformation of the quantum-mechanical Sine-Gordon and Double-Well potentials which we call the Double Sine-Gordon (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 Quasi-Exact-Solvability (QES) – and solvable to all orders in perturbation theory for TDW. For DSG such states do not show any instanton-like 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 all-orders perturbative states that are not normalizable, and hence, requires a non-perturbative energy shift. Both of these puzzles are solved by including complex saddles. 


Masahito Yamazaki, IMPU


Title: Conformal Blocks and Verma Modules


(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.

10-17-16 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 finite-dimensional toy model for non-linear heat-type 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 non-linear walls, on which asymptotics of the metric are described by nested logarithms.


Arnav Tripathy, Harvard University


Spinning BPS states and motivic Donaldson-Thomas 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 Yau-Zaslow formula for counts of rational nodal curves. In particular, I’ll give a string-theoretic derivation of the threefold’s motivic Donaldson-Thomas invariants given the Hodge-elliptic genus of the K3, a new quantity interpolating between the Hodge polynomial and the elliptic genus.


Joseph Minahan, Uppsala University


Supersymmetric gauge theories on $d$-dimensional spheres


In this talk I discuss localizing super Yang-Mills theories on spheres in various dimensions.  Our results can be continued to non-integer 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.


Seung-Joo Lee, Virginia Tech


Multiple Fibrations in Calabi-Yau Geometry and String Dualities


We study the ubiquity of multiple fibration structures in known constructions of Calabi-Yau manifolds and explore the role they play for string dualities. Upon introducing new tools for resolved Calabi-Yau varieties, we analyze a set of F-theory effective theories associated to the different elliptic fibrations and relate them via the M-/F-theory correspondence. Explicit geometric examples will include higher-rank Mordell-Weil groups and non-flat fibrations. In addition, in the context of heterotic/F-theory 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.


Thomas Walpuski, MIT

Title: Singular PHYM connections (on ACyl Kähler manifolds)


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^{n-1}.

This is joint work with A. Jacob and H. Sá Earp.


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 co-dimension 4 defects and their interaction with instanton particles. I will show that the partition function of this co-dimension 4 defect is related to Nekrasov’s qq-character. In the second part, I will talk about co-dimension 2 defects and instanton partition functions. I will also explain that the partition functions of the co-dimension 2 defects give rise to eigenfunctions of associated integral Hamiltonians.

 12-05-16 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.


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