Veranstaltungen am Mathematischen Institut

Abstract: The bottom homotopy group of a flat commutative algebra over the sphere spectrum inherits a delta-ring structure from the Tate-valued Frobenius of Nikolaus-Scholze, which plays a big role in the relationship between trace methods and prismatic cohomology. It is an interesting question how much of the E_infty ring structure is remembered by this delta-ring structure. In this talk, we present a modest step towards understanding this, by proving that there is a one-to-one correspondence between H_infinity ring structures on flat S-modules and delta-ring structures on their pi_0.

Abstract: The cohomology ring of moduli spaces of manifolds is an important object in geometric topology, as it classifies characteristic classes of manifold bundles. For even-dimensional manifolds, Galatius and Randal-Williams established a complete homotopy theoretic formula for this object after a certain stabilization procedure. In this talk, I will explain an odd-dimensional analog of Galatius and Randal-Williams' work in the context of odd-dimensional manifold triads. After stating this result, I will explain the strategy of proof and discuss some applications and examples.