Arithmetic geometry of character varieties
GyeongHyeon Nam (Ajou University)
Wednesday 2nd October 16:00-17:00 Maths 311B
Abstract
Character varieties are constructed from homomorphisms of the fundamental group of a space into an algebraic group G. In particular, when the fundamental group arises from a Riemann surface, these varieties are deeply connected to important areas of mathematics, such as the Yang-Mills equations, the P=W conjecture, and mirror symmetry.
The work of Hausel, Letellier, and Rodríguez-Villegas has sparked extensive research on character varieties through point-counting methods, particularly for G = GL_n.
In this talk, we will explore how these ideas extend to arbitrary reductive groups, beyond GL_n. This is based on joint work with Masoud Kamgarpour, Bailey Whitbread, and Stefano Giannini. If time permits, we will see the additive analogue of this story.
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