Topology SeminarSpeaker: Joachim Kock (UAB)
Title: Decomposition spaces, incidence algebras and Möbius inversion (background talk)
Date: 10/11/2026
Time: 15:00
Web: http://mat.uab.cat/~topalg
Abstract: Decomposition spaces, also called 2-Segal spaces, are simplicial spaces that generalise (nerves of) posets, monoids, categories, and operads, and they are supposed to be the most general setting supporting the construction of incidence (co)algebras and the Möbius inversion principle. The aim of the talk is to motivate the theory and explain the basic ideas. This is meant as background material for topics that may come up later in the seminar, in particular a talk at some point on quasi\-symmetric functions, and maybe talks on higher Segal spaces.
(This is old work with Imma Gálvez and Andy Tonks; the recommended entry point is the survey "Decomposition spaces in Combinatorics".)
Ring Theory SeminarSpeaker: Adriana Fernández Quero (KU Leuven)
Title: Non-amenable C$^*$-superrigid groups that are not W$^*$-superrigid
Date: 18/11/2026
Time: 15:00
Web: http://mat.uab.cat/web/ligat/
Abstract: Rigidity results for group operator algebras have unsurprisingly followed diverging paths in the settings of C$^*$-algebras and von Neumann algebras. Famously, group von Neumann algebras of icc amenable groups have no memory of the group, while C$^*$-superrigidity results have managed to tackle different classes of amenable groups. Although it is natural to expect there should exist a broader variety of non-amenable C$^*$-superrigid groups than W$^*$-superrigid, it was previously unknown whether there exist non-amenable groups that are C$^*$-superrigid but not W$^*$-superrigid. In joint work with Juan Felipe Ariza Mejía and Ionut Chifan, we bridge this gap by constructing a continuum of non-amenable groups exhibiting this phenomenon.