中科院数学与系统科学研究院
数学研究所
拓扑研讨班
报告人： 陈伟彦 博士（University of Minnesota）
题 目：Topology and Arithmetic Statistics
时 间：2019.12.11（星期三），10:30-11:30
地 点：数学院南楼N226室
摘 要：Topology studies the shape of spaces. Arithmetic statistics studies the behavior of random algebraic objects such as integers and polynomials. I will talk about a circle of ideas connecting these two seemingly unrelated areas. To illuminate the connection, I will focus on three concrete examples: (1) the Burau representation of the braid groups, (2) analytic number theory for effective 0-cycles on a variety, and (3) cohomology of the space of multivariate irreducible polynomials. These projects are parts of a broader research program, with contributions by topologists, algebraic geometers, and number theorists in the past decade, and lead to many future directions yet to be explored.
