Vorträge des SFB 1442

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Claudia Rüdiger

Josefien Kuijper (Utrecht University): The Dehn invariant for spherical scissors congruence as spectral Hopf algebra

Monday, 16.12.2024 14:15 im Raum M3

Mathematik und Informatik

Abstract: The Dehn invariant is known to many as the satisfying solution to Hilbert?s 3rd problem: a three-dimensional polyhedron P can be cut into pieces and reassembled into a polyhedron Q if and only if Q and P have not only the same volume, but also the same Dehn invariant. Generalised versions of Hilbert?s 3rd problem concern the so-called scissors congruence groups of euclidean, hyperbolic and spherical geometry in varying dimensions, and in these contexts one can define a generalised Dehn invariant. In the spherical case, Sah showed that the Dehn invariant makes the scissors congruence groups into a graded Hopf algebra. Zakharevich has shown that one can lift the scissors congruence group to a K-theory spectrum. In this talk I will discuss a lift of the Dehn invariant to the spectrum level, and we will see how it gives rise to a spectral version of Sah?s Hopf algebra. This talk is based on joint work in progress with Inbar Klang, Cary Malkiewich, David Mehrle and Thor Wittich.



Angelegt am 28.11.2024 von Claudia Rüdiger
Geändert am 28.11.2024 von Claudia Rüdiger
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Claudia Rüdiger

Ko Aoki (MPI Bonn): Solidification of algebraic K-theory

Monday, 06.01.2025 14:00 im Raum M3

Mathematik und Informatik

Abstract: Clausen?Scholze's condensed mathematics provides a framework for doing homological algebra in the presence of topology. A key notion is solidification, a completion process for condensed spectra (roughly, spectra equipped with a topology). In this talk, we consider the solidification of the algebraic K-theory of condensed algebras. I explain results that connect it to topological and semitopological K-theory. I then discuss Rosenberg's conjecture on the algebraic K-theory of operator algebras and suggest how condensed mathematics may offer new perspectives.



Angelegt am 25.11.2024 von Claudia Rüdiger
Geändert am 25.11.2024 von Claudia Rüdiger
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Jack Kelly (University of Oxford): Derived analytic geometry as bornological algebraic geometry

Monday, 20.01.2025 14:15 im Raum M3

Mathematik und Informatik

In this talk I will explain how derived analytic geometry, both Archimedean and non-Archimedean, can be realised as algebraic geometry relative to the monoidal category of bornological abelian groups of convex type. I will compare with existing models of derived analytic geometry, and suggest some applications.



Angelegt am 27.11.2024 von Claudia Rüdiger
Geändert am 27.11.2024 von Claudia Rüdiger
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