The Weil Conjectures and A1-homotopy Theory
University of Chicago Department of Mathematics via YouTube
Overview
Explore the fascinating intersection of algebraic topology and number theory in this colloquium talk by Kirsten Wickelgren from Duke University. Delve into the Weil conjectures, a groundbreaking set of propositions from 1948 that establish a profound connection between algebraic topology and solutions to equations over finite fields. Discover how the zeta function of a variety over a finite field serves as both a generating function for solution counts and a product of characteristic polynomials of cohomology group endomorphisms. Learn about A1-homotopy theory and its applications in this context. Examine an enriched version of the zeta function with coefficients in a group of bilinear forms, revealing new insights into the relationship between finite field solutions and the topology of associated real manifolds. Gain exposure to cutting-edge research in this field, presented in collaboration with Tom Bachmann, Margaret Bilu, Wei Ho, Padma Srinivasan, and Isabel Vogt.
Syllabus
Colloquium: Kirsten Wickelgren (Duke)
Taught by
University of Chicago Department of Mathematics