[Topology.beta] Topology Intercity Seminar next Thursday

[Klang, I. (Inbar)]

Dear all,

Next week, on Thursday 30 January, we will have the Topology Intercity Seminar (TopICS) here at the VU. The talks will take place in 9A46 from 13:00 to 17:00. Here is the schedule and abstracts; you can also find them on the website
https://guyboyde.wordpress.com/topics-schedule-2024-25/

Schedule:

13:00-14:00: Alba Sendón Blanco (VU)
Title: Scissors congruence K-theory for equivariant manifolds

Abstract: Imagine that you are given a manifold, a pair of scissors and some glue. With that material, are you able to get any other manifold? It is known that you can, as long as the initial and final manifolds have the same boundary and Euler characteristic. If now we talk about manifolds with actions of a finite group, we will see that the answer is not that easy. One can try to find help in homotopy theory to answer this question. I will explain how to set the equivariant cut-and-paste groups of manifolds in an algebraic K-theoretic environment. In particular, there is a K-theory spectrum that lifts the equivariant cut-and-paste groups and is the source of a spectrum level lift of the Burnside ring valued equivariant Euler characteristic. Moreover, the equivariant cut-and-paste groups for varying subgroups assemble into a Mackey functor, which is a shadow of a conjectural higher genuine equivariant structure. This talk is based on joint work with Mona Merling, Ming Ng, Julia Semikina and Lucas Williams [arXiv:2501.06928].


14:30-15:30: Teena Gerhardt (Michigan State)
Title: Topological Hochschild homology and equivariant algebraic structures

Abstract: Hochschild homology of a ring has a topological analogue for ring spectra, topological Hochschild homology (THH), which plays an essential role in the trace method approach to algebraic K-theory. Topological Hochschild homology is closely related to Witt vectors, and this relationship has facilitated algebraic K-theory calculations. For equivariant rings (or ring spectra) there is a theory of twisted topological Hochschild homology that builds upon Hill, Hopkins, and Ravenel's work on equivariant norms. This twisted THH is closely related to an equivariant version of Witt vectors. Indeed, in this talk I will discuss recent work showing that the equivariant homotopy of twisted THH forms an equivariant Witt complex. This is joint work with Bohmann, Krulewski, Petersen, and Yang.



16:00-17:00: Nima Rasekh (Universität Greifswald)
Title: From Internal Higher Categories to the Foundation of Mathematics

Abstract: Internal categories extend the concept of ordinary categories, enabling the application of categorical methods across diverse contexts, from Lie groupoids to condensed categories. A particularly elegant use of internal category theory arises in higher categorical sheaf theory, having resulted in powerful ∞-categorical techniques and results internal to Grothendieck ∞-topoi. In this talk, we seek to generalize several results to more general internal ∞-categories, only to encounter unexpected challenges that surprisingly intertwine ∞-category theory with the foundations of mathematics.
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