06.11.2024, 14:00 - 16:00
– Campus Golm, Building 9, Room 2.22 and via Zoom
Institutskolloquium
Graphon Models for Inhomogeneous Random Graphs
Olga Klopp (Paris), Nicolas Verzelen (Montpellier)
Georg Lehner (FU Berlin)
The Rosenberg Conjecture through the lens of Solidification
The Rosenberg Conjecture states that for a given Banach Algebra A, the
comparison map between algebraic and topological K-theory becomes an
isomorphism on finite coefficients. The new framework of condensed
mathematics developed by Scholze et.al. allows one to frame this question
in a different way. Condensed sets are a replacement for topological
spaces that work well in their interplay with algebraic constructions. In
particular, if we view our Banach algebra A as a condensed ring, we can
equip the algebraic K-theory groups of A with the structure of condensed
abelian groups. There exists a natural notion of completion for condensed
abelian groups called solidification. The map from the K-theory of A into
its solidification recovers the comparion map from algebraic to
topological K-theory, allowing one to phrase the Rosenberg conjecture as a
topological statement about the condensed structure of the K-theory of A.