Mittagsseminar zur Arithmetik: Vaughan McDonald (Stanford): Eigenvarieties over CM fields and trianguline representations
Tuesday, 15.04.2025 10:15 im Raum SRZ 216/217
Eigenvarieties are parameter spaces of certain p-adic automorphic forms of varying weights. Part of the p-adic Langlands program aims to relate eigenvarieties to spaces of trianguline Galois representations, which contain all crystalline Galois representations. For definite unitary groups, this connection has been developed extensively. Our goal is to consider p-adic automorphic forms without self-duality conditions. Namely, we prove that many eigenvarieties for the group GL_n over a CM field have associated Galois representations which are trianguline. Our proof strategy is to realize such eigenvarieties inside a single eigenvariety for a unitary group, which might be of independent interest.
Angelegt am 10.04.2025 von Heike Harenbrock
Geändert am 10.04.2025 von Heike Harenbrock
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Philipp Sibbel: C*-diagonals with Cantor spectrum in Cuntz algebras. Oberseminar C*-Algebren.
Tuesday, 15.04.2025 16:15 im Raum SRZ 216/217
A Cartan subalgebra exists in every classifiable C*-algebra, and in particular, every classifiable C*-algebra which is stably finite, contains a C*-diagonal. However, not much is known about the existence of C*-diagonals in Kirchberg algebras. I will give an overview and explain how to construct Cantor spectrum C*-diagonals in the Cuntz algebra O_k when k finite.
Angelegt am 08.04.2025 von Elke Enning
Geändert am 08.04.2025 von Elke Enning
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Mittagsseminar zur Arithmetik: Arthur-César Le Bras (Université de Strasbourg): Analytic prismatization
Tuesday, 22.04.2025 10:15 im Raum SRZ 216/217
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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Sam Shepherd: Product separability for special cube complexes. Oberseminar C*-Algebren.
Tuesday, 22.04.2025 16:15 im Raum SRZ 216/217
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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Wilhelm Killing Kolloquium: Prof. Dr. Katharina Hübner (Goethe Universität Frankfurt): Paths in nonarchimedean spaces
Thursday, 24.04.2025 14:15 im Raum M4
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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Thomas Tony (University of Potsdam): Higher Index Theory and Scalar Curvature Rigidity
Monday, 28.04.2025 01:00 im Raum SR 1C
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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