A finite geometry problem from some conjectures of Brauer

Prof. Michael Geline
Professor of Mathematics
Northern Illinois University

We will begin with a problem in “finite geometry” which captures at least some of the spirit of algebraic geometry in positive characteristic. More specifically, we will solve an elementary problem about vector spaces over the integers (mod p) by looking at sums of complex roots of unity. We will then see how this problem arose from a conjectured local to global principle in the representation theory of finite groups.