Termine

Topological Hochschild homology (THH) has been used successfully to construct prismatic cohomology, the most powerful cohomology theory that we currently have for formal schemes over Z_p. But for rigid-analytic varieties over Q_p, or even global objects like varieties over Q, THH is less useful: For rational inputs, THH will always vanish modulo p, and so it can't have any interesting comparisons to, say, étale cohomology with torsion coefficients. In this talk, I'll explain a refinement of THH (due to Efimov and Scholze) that overcomes these issues, and I'll show a few promising computations. I'll also sketch how one should be able to recover Scholze's analytic Habiro cohomology from refined THH.

Abstract: I will speak on the classification problem of compact homogeneous Einstein spaces G/H. Recall that a G-invariant Einstein metric can be characterized as a critical point of the scalar curvature function restricted to the space of G-invariant metrics of volume one. To this end, I will introduce a new simplicial complex (defined by certain intermediate subgroups H

First I recall the construction of the p-adic Deligne--Lusztig stack attached to a (quasi-split) p-adic reductive group G/Q_p. The fibers of this stack over Isoc_G are p-adic DL-spaces which in turn contain parahoric DL-varieties. Their cohomology is a source for interesting (smooth) representations (of parahoric subgroups) of G(Q_p). I will explain two applications to the study of supercuspidal representations: (1) construction of some new supercuspidals, (2) computation, based on a theorem of T. Feng, of Fargues--Scholze parameters of some supercuspidals. There results are based on several joint works with O. Dudas, S. Nie, P. Tan.

A complex valued function f:(M,g) \to \C$ is said to be a $(\lambda,mu)$-eigenfunction if it is eigen with respect to both the Laplace-Beltrami operator and the conformality operator kappa(f,f) = g(\nabla f,\nabla f). Recent developments have shown that $(\lambda,\mu)$-eigenfunctions can be used in the construction of harmonic morphisms, proper r-harmonic maps, and minimal submanifold of codimension two. There has also been interest in classifying eigenfunctions. In this talk we consider the case when (M,g) is a compact Lie group equipped with a bi-invariant metric, as the Laplace-Beltrami operator's spectral theory is described by the Peter-Weyl theorem. We use the Peter-Weyl theorem, and other representation theoretic techniques in order to classify all the pairs (\lambda, \mu) as well as describe conditions which ensure the existence of eigenfunctions. Finally, we produce new eigenfunctions on both compact Lie groups G and Riemannian symmetric spaces G/K. This is a joint project with Oskar Riedler. If you are interested please contact Prof. Dr. Anna Siffert (asiffert@uni-muenster.de)

Partial group actions on spaces by homeomorphisms between open sets provide a rich class of C*-algebras via the crossed product construction. We start an in-depth investigation when a general Hausdorff étale groupoid is a transformation groupoid by a partial action. Our negative results contain the first examples of Hausdorff étale groupoids which do not arise as transformation groupoids of partial group actions and which are not inner amenable in the sense of Anantharaman-Delaroche. On the positive side, we prove that many higher rank graph algebras as well as many unital UCT Kirchberg algebras can be realized via partial group actions. This is joint work with Alcides Buss.

Kolloquium über Geschichte und Didaktik der Mathematik

via zoom If you are interested please contact Prof. Dr. Anna Siffert (asiffert@uni-muenster.de)