Medgar Evers College Mathematics Colloquium Fall 2021
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Wednesday October 27
Pedro Vaz (Catholic University of Louvain)
Title: Categorification of Verma Modules in low-dimensional topology
Abstract: I will review the program of categorification of Verma modules and explain one of their possible applications to low-dimensional topology, namely to the construction of a Khovanov invariant for links in the solid torus via a categorification of the blob algebra.This is the result of collaborations with Abel Lacabanne and Grégoire Naisse.
Monday November 29
Paul Wedrich (University of Hamburg)
Title: Homology theories in quantum topology
Abstract: The last two decades have seen the rise of powerful homological and categorical techniques in low-dimensional topology, which have led to the development of a novel class of invariants of knots, links, braids, and manifolds of dimensions 3 and 4. These invariants are controlled by higher algebraic structures, through which they are connected to a broad range of research areas in modern mathematics and physics. This talk will introduce Khovanov homology as an access point to this research area, and then proceed to survey recent developments, illustrate applications, and outline future directions.