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Integrable line defects and 4d Chern-Simons theory
I discuss an application of a recent construction of 2d integrable field theories from 4d Chern-Simons theory by Costello and Yamazaki. After a review of the construction, I consider integrable...
Oct 17, 2019
Equivariant localization and Atiyah-Segal completion for Hochschild and cyclic homology
There is a close relationship between derived loop spaces, a geometric object, and Hochschild homology, a categorical invariant, made possible by derived algebraic geometry, thus allowing for both intuitive insights...
Oct 24, 2019
3D Mirror Symmetry and HOMFLY-PT Homology
A recent construction of HOMFLY-PT knot homology by Oblomkov-Rozansky has its physical origin in “B-twisted” 3D N=4 gauge theory, with adjoint and fundamental matter. Mathematically, the construction uses certain categories...
Oct 31, 2019
Bridgeland stability conditions relative to a boundary
In this talk I will present a construction of relative Bridgeland stability conditions that appeared in my work on stability of topological Fukaya categories of surfaces. This construction gives a...
Nov 07, 2019
The Diamond Lemma for (multiplicative) preprojective algebras
Bergman's Diamond Lemma for ring theory gives an algorithm to produce a (non-canonical) basis for a ring presented by generators and relations. After demonstrating this algorithm in concrete, geometrically-minded examples...
Nov 14, 2019
On the classification of topological phases
There is a rich interplay between higher algebra (category theory, algebraic topology) and condensed matter. I will describe recent mathematical results in the classification of gapped topological phases of matter...
Jun 01, 2020
Protected spin characters, link invariants, and q-nonabelianization
In this talk I will describe a new link "invariant" (with certain wall-crossing properties) for links L in a three-manifold M, where M takes the form of a surface times...
Sep 17, 2020
On the geometry of nodal domains for random eigenfunctions on compact surfaces
A classical result of R. Courant gives an upper bound for the count of nodal domains (connected components of the complement of where a function vanishes) for Dirichlet eigenfunctions on...
Oct 01, 2020
Quasimaps and BPS counts
The theory of quasimaps to Nakajima quiver varieties X has recently been used very effectively by Aganagic, Okounkov and others to study symplectic duality. For certain X, namely Hilbert schemes...
Oct 08, 2020
Toric mirror symmetry via GIT windows
Every toric variety is a GIT quotient of an affine space by an algebraic torus. In this talk, I will discuss a way to understand and compute the symplectic mirrors...
Oct 15, 2020