Property (T), sums of square and numerical certificates

Piotr Nowak (Institute of Mathematics of the Polish Academy of Sciences) https://simons.berkeley.edu/talks/piotr-nowak-institute-mathematics-polish-academy-sciences-2026-09-21 Local to Global Principles This talk will be a gentle introduction to the topic of property (T) and algebraic spectral gaps. We will begin by giving a brief overview of property (T) and move on to Ozawa’s characterization via an algebraic spectral gap for the group Laplacian in the augmentation ideal. Then I will describe a numerical approach to proving property (T) via such sums of squares and discuss certification, which turns an approximate numerical solution into the existence of a true, exact solution. This approach has led to new proofs of property (T) for classical examples such as SL_n(Z), n＞2, and proving property (T) for Aut(F_n), n＞3.