Speaker: Allen Yuan (MIT)
Title: An equivariant Segal conjecture
Abstract: For a finite group G, the Segal conjecture describes the space of stable maps from BG to a point. When G is a cyclic group of prime order, work of Miller, Lunøe-Nielsen-Rognes, and Nikolaus-Scholze generalizes this to an assertion about the Tate diagonal on any spectrum X. I will discuss the statement of and partial progress on a common generalization of these results, which makes reference to a finite group G, subgroup H, and genuine H-spectrum X. Time permitting, I will discuss consequences of this work for genuine equivariant coalgebras, the coalgebra Frobenius, and models for the homotopy theory of spaces.