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Virtual Classes of Representation Varieties of Upper Triangular Matrices via Topological Quantum Field Theories

ALGEBRAIC GEOMETRY & NUMBER THEORY SEMINAR

Date: Thursday, October 15, 2020 14:00 - 16:00
Speaker: Márton Hablicsek (Universiteit Leiden, NL)
Location: https://mathseminars.org/seminar/AGNTISTA
Series: Mathematics and CS Seminar
Host: Tamas Hausel

Let $X$ be an oriented closed connected surface. The set of group representations from the fundamental group of $X$ to an algebraic group $G$ has a structure of an algebraic variety. This variety is called the $G$-representation variety of $X$. In this talk, I will use a geometric method developed by González-Prieto, Logares, Muñoz, and Newstead to compute the virtual classes of $G$-representation varieties where $G$ is the group of complex upper-triangular matrices of rank 2, 3, or 4. This is joint work with Jesse Vogel.


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