Braids, algebraic curves, and 0-cycles

Weiyan Chen
University of Minnesota, Twin Cities
Friday, September 15, 2017 -
2:30pm to 3:30pm
Vincent Hall 207

We will see how ideas from topology can provide different perspectives on problems in arithmetic via the bridge of étale cohomology. I will present two concrete examples: (1) how braid groups and Burau representations (topology) could help one count points on algebraic curves over finite fields (arithmetic), and (2) how topology would lead to generalizations of the well-known analogy between integers and polynomials, and results about "analytic number theory for effective 0-cycles on varieties over finite fields".