Confronting Thompson’s Conjecture: A Hypercontractive Approach

This proposal concerns enhancing our understanding of linear algebraic group via methods from Boolean function analysis.

In particular, it is focused on addressing Thompson's conjecture about conjugacy classes, a longstanding problem in group theory that has captivated researchers for over four decades.

We bring together insights from diverse disciplines, weaving together concrete conjectures concerning character value bounds, the independence number of normal Cayley graphs, and most critically, the novel concept of hypercontractivity in groups to provide a framework for a solution to the conjecture.