Vorträge des SFB 1442

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Heike Harenbrock

Mittagsseminar zur Arithmetik: Arthur-César Le Bras (Université de Strasbourg): Analytic prismatization

Tuesday, 22.04.2025 10:15 im Raum SRZ 216/217

Mathematik und Informatik

In joint work, very much in progress, with Johannes Anschütz, Juan Esteban Rodriguez Camargo and Peter Scholze, we define an analogue of prismatic cohomology for rigid analytic varieties. Our construction is formulated using analytic stacks and takes inspiration both from Scholze's theory of diamonds and the work of Bhatt-Lurie and Drinfeld on the prismatization of p-adic formal schemes. It also furnishes a potential formulation of the geometrization of the p-adic local Langlands correspondence. In this talk, I would like to survey various aspects of this work.



Angelegt am 10.04.2025 von Heike Harenbrock
Geändert am 10.04.2025 von Heike Harenbrock
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Elke Enning

Sam Shepherd: Product separability for special cube complexes. Oberseminar C*-Algebren.

Tuesday, 22.04.2025 16:15 im Raum SRZ 216/217

Mathematik und Informatik

I will talk about my recent result regarding the separability of products of subgroups in virtually special cubulated groups. My talk will also contain lots of background on cube complexes, cubulated groups and (virtual) specialness, which has been an important topic in geometric group theory over the last 20 years, particularly with the connection to 3-manifold theory.



Angelegt am 10.04.2025 von Elke Enning
Geändert am 10.04.2025 von Elke Enning
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Oberseminare und sonstige Vorträge
Vorträge des SFB 1442
Veranstaltungen am Mathematischen Institut
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Claudia Rüdiger

Maria Yakerson (IMJ-PRG, Sorbonne): Fun facts about p-perfection

Wednesday, 23.04.2025 14:00 im Raum SRZ 216/17

Mathematik und Informatik

Abstract: In this talk we will discuss the structure of $\mathbb E_\infty$-monoids on which a prime $p$ acts invertibly, which we call $p$-perfect. In particular, we prove that in many examples, they almost embed in their group-completion. We further study the $p$-perfection functor, and describe it in terms of Quillen's $+$-construction, similarly to group completion. This is joint work with Maxime Ramzi.



Angelegt am 14.04.2025 von Claudia Rüdiger
Geändert am 14.04.2025 von Claudia Rüdiger
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Claudia Lückert

Wilhelm Killing Kolloquium: Prof. Dr. Katharina Hübner (Goethe Universität Frankfurt): Paths in nonarchimedean spaces

Thursday, 24.04.2025 14:15 im Raum M4

Mathematik und Informatik

If we complete the rational numbers $\mathbb{Q}$ with respect to the standard absolute value, we obtain the reals $\mathbb{R}$, wich is a connected topological space. The completion $\mathbb{Q}_p$ of $\mathbb{Q}$ with respect to the $p$-adic valuation for a prime $p$, however, is totally disconnected. So it seems that the concept of a path connecting two points in the $p$-adic numbers $\mathbb{Q}_p$ (or $\mathbb{Q}_p^n$) does not make sense. In fact, the space $\mathbb{Q}_p$ itself is not quite suitable for doing geometry. Instead one can consider the affine line $\mathbb{A}_{\mathbb{Q}_p}^1$ as an adic space. It contains $\mathbb{Q}_p$ as so called \emph{classical points} but has many more points. In this talk we will convince ourselves that $\mathbb{A}_{\mathbb{Q}_p}^1$ is indeed path connected if we use the right notion of a path.



Angelegt am 17.03.2025 von Claudia Lückert
Geändert am 09.04.2025 von Claudia Lückert
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Kolloquium Wilhelm Killing
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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Oberseminare und sonstige Vorträge
Vorträge des SFB 1442
Veranstaltungen am Mathematischen Institut