1. 일시 : 2022년 5월 27일 (금) 15:30-16:30
2. 장소 : Zoom을 이용한 실시간 온라인 강연
3. 연사 : 남경현 (호주 퀸즐랜드대학교 박사과정)
4. 제목 : Arithmetic of character variety of reductive groups
5. 초록 : Counting the number of points on a variety is a historical method for investigating the variety, for example, in the Weil conjecture. Nowadays, it is known that the point count helps us determine the E-polynomial. This E-polynomial, in turn, gives arithmetic-geometric information on the variety such as the dimension, the number of irreducible components and Euler characteristic.
In this talk, we will consider a specific type of variety, the character variety associated to the fundamental group of a surface. In short, we will discuss this variety for a punctured surface, with regular semisimple or regular unipotent monodromy at the punctures.
This variety plays a crucial role in diverse areas of mathematics, including non-abelian Hodge theory, geometric Langlands program and mathematical physics. The complex representation theory of finite groups will be used to compute the number of points on such a variety.