Abstract: This is a continuation of the previous talk about skein lasagna modules. We review some features of the Khovanov homology and its Lee deformation. We examine the resulting skein lasagna modules with these two theories as inputs, extract a lasagna version of Rasmussen’s s-invariant, and state some formal properties. We then show that Khovanov/Lee skein lasagna modules and lasagna … Read More

Abstract: Skein lasagna modules are invariants of smooth 4-dimensional manifolds capable of detecting exotic phenomena. Wall-type stabilization problems ask about the behavior of exotic phenomena under various topological operations. In this talk, we will describe the invariants we use and the necessary properties. We describe, with Wall-type external stabilization problems as motivation, a method for computing the Khovanov skein lasagna module of $S^2 … Read More

Abstract: In 2017, Braverman-Finkelberg-Nakajima gave a precise definition of the Coulomb branch of a 3d N = 4 supersymmetric gauge theory of cotangent type associated to a complex reductive group G and a finite dimensional complex representation N. In our first part of this talk, we will recall the definition and basic properties of such Coulomb branches, as well as … Read More

A basic question in classical gauge theory is to describe moduli spaces of solutions to PDEs arising in that context (such as Bogomolny equations on R^3 or anti-self-duality equations on R^4), at least as complex manifolds, in explicit finite-dimensional terms. In the case of Bogomolny equations, a powerful means to do this is provided by the scattering data assigned to … Read More

Instanton scattering matrices constructed in the previous talk give evidence for the existence of an R-matrix (re)construction of quantized Coulomb branch algebras of 3d N=4 quiver gauge theories using the (shifted) Yangian associated to the quiver. In this talk I will report on progress in putting this in a more standard context for geometric construction of Yangian actions, using critical … Read More

Abstract: We introduce a new class of smooth correspondences between Nakajima quiver varieties called split parabolic quiver varieties, and study their properties. We also construct some interesting operators in  equivariant K-theory of these varieties, and relate them to K-theoretic Hall algebra  and double Dyck path algebra. This is a joint work with Nicolle Gonzalez and Jose Simental.