[Topology.beta] TopICS on October 31, Nijmegen

[Klang, I. (Inbar)]

Dear all,

Please see below for details on this Friday's Topology Intercity Seminar. Regrettably, this clashes with DDT&G this time.

________________________________
From: TopICS-l <topics-l-bounces at lists.science.uu.nl> on behalf of Subramanian, V. (Vignesh) via TopICS-l <topics-l at lists.science.uu.nl>
Sent: Friday, October 17, 2025 4:06 PM
To: topics-l at lists.science.uu.nl <topics-l at lists.science.uu.nl>
Subject: [TopICS-l] TopICS on October 31, Nijmegen


Dear all,

Hope you are doing well. Here are the details of the first TopICS meeting this semester in Nijmegen.



  *   Date: Friday, October 31
  *   Time: 13:30 to 17:30
  *   Place: Nijmegen Huygensgebouw, Room: HG00.303



  *   Speakers and abstracts

  1.  Steffen Sagave (13:30 - 14:30)

Title: Logarithmic Topological Cyclic Homology



Abstract: Forming the fraction field of an integral domain is a classical construction in algebra. The generalization of this notion to structured ring spectra is less obvious because inverting all non-zero homotopy classes often leads to a too drastic localization. For the connective complex topological K-theory spectrum and the connective Adams summand, computations by Ausoni and Rognes suggest that a fraction field may be realized as a logarithmic ring spectrum with logarithmic structure generated by a given prime and the Bott element. In this talk, I will introduce logarithmic ring spectra, their topological Hochschild homology, and their topological cyclic homology, and I will show how localization sequences for these theories help to identify a good candidate for a fraction field of topological K-theory spectra.



This is report on joint work in progress with John Rognes and Christian Schlichtkrull.



       2. Luca Pol (15:00-16:00)



Title: New Phenomena in the tt-geometry of global representations



Abstract:  A global representation over a field is a compatible collection of representations of the outer automorphism groups of the groups belonging to some collection of finite groups U. Global representations assemble into an abelian category AU which simultaneously generalizes classical representation theory and the category of VI-modules appearing in the representation theory of the general linear groups. The derived category of global representations D(U) is an example of a non-rigid compactly generated tensor-triangulated category, which is known to be equivalent to the category of rational global spectra for the family U. In this talk I would like to present some new phenomena that we encounter and explain some calculations of the Balmer spectrum in this setting. This is based on joint work with Miguel Barrero, Tobias Barthel, Neil Strickland and Jordan Williamson.



           3. Kathryn Hess ( 16:30-17:30)



Title: From group actions to actegories.



Abstract: The notions of group action and of module over a ring can be categorified to that of an actegory, consisting essentially of a functorial action of a monoidal category on a (2-)category.  I will describe several interesting examples of actegories and of morphisms between them, in particular arising from group actions, and also explain how to see (homotopy) colimits and limits as morphisms between two different actegory structures on the 2-category of categories.  I’ll conclude by explaining how this type of actegory morphism can be used to build a machine that produces monads or comonads, like those that are central to the construction of the discrete calculus of Bauer-Johnson-McCarthy.



Joint work with Kristine Bauer, Brenda Johnson, and Julie Rasmussen




Looking forward to meeting you in Nijmegen.



Best regards,

Ahina and Vignesh
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