Vorträge des SFB 1442

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Claudia Rüdiger

Thomas Tony (University of Potsdam): Higher Index Theory and Scalar Curvature Rigidity

Monday, 28.04.2025 01:00 im Raum SR 1C

Mathematik und Informatik

Abstract: Llarull proved in the late '90s that the round n-sphere is area-extremal, meaning that one cannot simultaneously increase both its scalar curvature and its metric. Goette and Semmelmann generalized Llarull's rigidity statement to certain area-non-increasing spin maps $f\colon M\to N$ of non-zero $\hat{A}$-degree. In this talk, I will begin with a brief introduction to scalar curvature comparison geometry and review the Dirac operator method. I will then explain how higher index theory can be used to generalize classical extremality and rigidity statements. More specifically, I will present a recent generalization of Goette and Semmelmann?s theorem, in which the topological condition on the $\hat{A}$-degree is replaced by a weaker condition involving the so-called higher mapping degree. A key challenge in the proof is that, in general, a non-vanishing higher index does not necessarily give rise to a non-trivial kernel of the corresponding Dirac operator. I will present a new method that extracts geometrically useful information even in this more general setting.



Angelegt am 09.04.2025 von Claudia Rüdiger
Geändert am 09.04.2025 von Claudia Rüdiger
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Oberseminare und sonstige Vorträge
Vorträge des SFB 1442
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Claudia Rüdiger

Leopold Zoller (Universität zu Köln): Integral aspects of the Chang-Skjelbred method

Monday, 28.04.2025 16:00 im Raum SR 4

Mathematik und Informatik

Abstract: The Chang-Skjelbred method is a popular technique to compute the the (equivariant) cohomology of a space with a certain type of torus action. While traditionally employed for coefficients in fields of characteristic 0, the strategy is apt for integral calculations as well under the right conditions. We will give an overview over the method and in particular discuss integral developments and applications.



Angelegt am 09.04.2025 von Claudia Rüdiger
Geändert am 09.04.2025 von Claudia Rüdiger
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Elke Enning

Milan Donvil (KU Leuven): W*-superrigidity for cocycle twisted group von Neumann algebras. Oberseminar C*-Algebren.

Tuesday, 29.04.2025 16:15 im Raum SRZ 216/217

Mathematik und Informatik

A group is called W*-superrigid if its group von Neumann algebra completely remembers the original group. In this talk I will present a joint work with Stefaan Vaes in which we generalize W*-superrigidity for groups in two directions. Firstly, we find a class of groups for which W*-superrigidity holds in the presence of a twist by an arbitrary 2-cocyle: the twisted group von Neumann algebra completely remembers both the original group and the 2-cocycle. Secondly, for the same class of groups, the superrigidity also holds up to virtual isomorphism. If time permits, I will moreover explain how this result and the technical machinery behind it led to other new W*-superrigidity theorems in two different contexts.



Angelegt am 07.04.2025 von Elke Enning
Geändert am 10.04.2025 von Elke Enning
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Vorträge des SFB 1442
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Claudia Lückert

Wilhelm Killing Kolloquium: Prof. Dr. Annette Werner (Goethe Universität Frankfurt): The p-adic Simpson correspondence for torsors under commutative groups

Wednesday, 30.04.2025 14:15 im Raum SRZ 216/217

Mathematik und Informatik

Let X be a proper, smooth rigid space and G a commutative rigid group. We study the relationship between G-representations of the fundamental group of X and G-Higgs bundles on X. This is joint work with Ben Heuer and Mingjia Zhang.



Angelegt am 17.03.2025 von Claudia Lückert
Geändert am 07.04.2025 von Claudia Lückert
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Kolloquium Wilhelm Killing
Vorträge des SFB 1442
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Elke Enning

Keivan Mallahi Karei (Constructor University Bremen): Random free semigroups of affine transformations. Oberseminar C*-Algebren.

Tuesday, 06.05.2025 16:15 im Raum M4

Mathematik und Informatik

The question of the existence of free subgroups in a given group traces back to a problem posed by von Neumann. When such subgroups exist, their genericity has been the focus of extensive research. In this talk, we formulate and investigate a version of the genericity question for subgroups of the affine group over a field of characteristic zero. Let $G$ denote the affine group over a field $F$, and let $\mu$ be a probability measure on $G \times G$. Consider the left or right random walk $(X_n, Y_n)$ on $G \times G$ driven by $\mu$. I will discuss several results on conditions under which the semigroup generated b $X_n$, $Y_n$ is free, either eventually or infinitely often. The talk is based on a work in progress with Richard Aoun.



Angelegt am 07.04.2025 von Elke Enning
Geändert am 08.04.2025 von Elke Enning
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Vorträge des SFB 1442
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