Tufts Algebra, Geometry, and Number Theory Seminar
2023-03-16
Title: Brauer’s height zero conjecture
Pham Huu Tiep (Rutgers University / Princeton University/ MIT)
Abstract: Richard Brauer’s height zero conjecture (from 1955) predicts that, for any finite group \(G\) and prime \(p\), certain arithmetical properties of the degrees of complex irreducible representations of \(G\) within a \(p\)-block \(B\) are controlled by its defect groups. Building on work of many mathematicians, one part of the conjecture was finally proved by Kessar and Malle in 2013; however, the other part of the conjecture remained open. In this talk, we will discuss the recent proof of this remaining part of the conjecture. This is joint work with Malle, Navarro, and Schaeffer Fry.