Vivek Shende ( UC Berkeley and Syddansk Universitet) “Remarks and questions around geometric langlands and homological mirror symmetry “
Recent advances around Fukaya categories can be used to (mathematically rigorously) produce sheaves on Bun_G from smooth fibers of Hitchin fibrations. The resulting sheaves are presumably Hecke eigensheaves; I’ll explain why I don’t know how to prove this, and discuss various related questions.
Pavel Putrov ( ICTP “The Abdus Salam International Centre for Theoretical Physics”) in Trieste, Italy- “Counting solutions of Kapustin-Witten equations on a 3-manifold times a line”
In my talk I will first review the interpretation of the counts of solutions of Kapustin-Witten equations on a 3-manifold times a line as Stokes coefficients associated to the perturbative expansion of Chern-Simons theory. These counts can be naturally combined into q-series with integral coefficents, labelled by an ordered pair of flat connections. I will then present an explicit algorithm/formula … Read More
Lev Rosansky (UNC) ” Link homology from a B-twisted stack of D2 branes”
Abstract: Link homology is the space of states of BPS particles in a special 5d QFT. The BPS particles can be presented as D2 branes attached to Chern-Simons-related D4 branes and link-related NS5 branes. We assume that D2 branes form a stack split into domains by D4 and NS5 interfaces. The vibrations of the stack are described by a 3d … Read More
Jonathan Heckman (University of Pennsylvania) “Top Down Approach to Categorical Symmetries”
Abstract: Top down (i.e., stringy) constructions of quantum field theories provide a general template for constructing and studying a wide variety of different strongly coupled systems which are otherwise difficult to study using “textbook” methods based on perturbation theory of a Lagrangian field theory. In this talk we use the geometry of extra dimensions in string theory to study generalized … Read More
Pierrick Bousseau (UGA) “Donaldson-Thomas Invariants and Holomorphic Curves”
Abstract: Kontsevich and Soibelman suggested a correspondence between Donaldson-Thomas invariants of Calabi-Yau 3-folds and holomorphic curves in complex integrable systems. After reviewing this general expectation, I will present a concrete example related to mirror symmetry for the local projective plane (partly joint work with Descombes, Le Floch, Pioline), along with applications in enumerative geometry (partly joint work with Fan, Guo, … Read More
String Math: Spencer Tamagni (UC Berkeley) “Stable Envelopes for Vortex Moduli Spaces “
Abstract: Stable envelopes are correspondences useful for constructing geometric action of quantum groups and solutions to quantum Knizhnik-Zamolodchikov (qKZ) equations. I will review basic aspects of this and explain the construction in a novel class of examples consisting of certain vortex (also known as quasimap) moduli spaces. The main technical result is that K-theoretic curve counts in these varieties are controlled … Read More
String Math Seminar: Andrei Negut (MIT) “Quivers on the torus and quantum loop groups”
Abstract: Deeper structures behind BPS counting on toric Calabi-Yau 3-folds have recently been realized mathematically in terms of the quantum loop group associated to a certain quiver drawn on a torus, which is endowed with an action on the BPS vector space via crystal melting. In this talk, we identify the annihilator of the aforementioned action, thus leading to the … Read More
Sergey Cherkis (Arizona) “Exploded Geometry of Monopole Moduli Spaces”
Abstract: Computing the L2 cohomology of moduli spaces of monopoles and instantons is a challenging problem. It is significant in physics having an interpretations as counting the BPS states in quantum gauge theories, as well as in mathematics, manifesting itself in the geometric Langlands correspondence for complex surfaces. We propose a rather unconventional compactification of these moduli spaces … Read More
String Math Seminar: Denis Nesterov (University of Vienna) “Quasimaps to moduli spaces of sheaves and related topics”
Abstract: The minicourse will be comprised of three talks, which can be summarized by the slogan “Donaldson-Thomas theory of Surface x Curve = Gromov-Witten theory of moduli spaces of sheaves on Surface”.
Denis Nesterov (University of Vienna) “Quasimap wall-crossing, Vertex and applications”
In the second talk, using quasimaps, we establish a very general wall-crossing formula relating Donaldson-Thomas theory of Surface x Curve and Gromov-Witten theory of moduli spaces of sheaves on Surface. The wall-crossing is governed by Vertex (also known as I-function). We then discuss the old and the new instances of this wall-crossing.