13h30 Bjorn Dundas : Yet another approach to the K-theory of complex cobordisms
Ongoing work joint with Paul Arne Østvær
Motivic calculations sometimes facilitate calculations in topology and sometimes they shed light on relations that initially appear mysterious. The calculations of motivic Hochschild homology (MHH) of low chromatic height have mostly been of the latter type, where a lot of zeros in topology have appeared as torsion. The torsion is due to the tension between the topological circle and G_m, which I may comment on if time permits, but the main message in this talk is that the torsion actually holds valuable information. Indeed, climbing up the chromatic tower to cobordism we find that the torsion classes are placeholders for non-torsion in MHH(MGL). Equivariantly, however, torsion reappears.
In this talk I plan to outline yet another approach to the K-theory K(MU), or rather TC(MU), by working motivically over the complex numbers, which potentially can compete or work in tandem with existing approaches (some of which use the word “motivic” in a different sense).
14h45 Filipp Buryak : Representation stability of the spaces of string links
Because spaces of string links possess highly non-trivial symmetric group actions, their homology fail to stabilise in the classical sense. Church and Farb's theory of representation stability provides a modern algebraic framework to study such sequences of representations.
In this talk, I will start by introducing the key concepts of representation stability before shifting focus to Goodwillie-Weiss embedding calculus. Specifically, we will look at the combinatorial rational models for embedding spaces developed by Fresse, Turchin, and Willwacher, and see how these models allow us to deduce representation stability for the spaces of string links.
16h00 Yuri Sulyma : RO(G)-graded norms for de Rham-Witt forms
Equivariant homotopy theory is closely connected to p-adic cohomology via topological Hochschild homology (THH) and its variants. Two foundational computations in this field are: Bhatt-Morrow-Scholze related TC^- and TP of quasiregular semiperfectoid rings to prismatic cohomology, while Hesselholt related TR of smooth algebras over perfectoid rings to the de Rham-Witt complex.
I will explain RO(G)-graded generalizations of both of these computations, opening the door to more genuine-equivariant ideas in the field. In particular, we generalize Angeltveit's norm map of Witt vectors to the de Rham-Witt complex. | 
