Idisplays

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Sandra Huppert

Oberseminar Differentialgeometrie: Oskar Riedler (Universität Münster), Vortrag: Eigenfamilies and polynomial harmonic morphisms

Monday, 24.06.2024 16:00 im Raum SRZ 214

Mathematik und Informatik

Abstract: Complex valued harmonic morphisms are interesting maps that foliate their domain by minimal surfaces of co-dimension 2. In this talk we discuss the relation of homogeneous polynomial harmonic morphisms to so called eigenfamilies on spheres, and briefly describe recent classification efforts.



Angelegt am 07.03.2024 von Sandra Huppert
Geändert am 04.06.2024 von Sandra Huppert
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Oberseminare und sonstige Vorträge
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Anke Pietsch

Tee-Seminar: Dr. Kevin Klinge (KIT Karlsruher Institut für Technololgie): ?-Invariants and nilpotent groups

Monday, 24.06.2024 14:15 im Raum SR1C

Mathematik und Informatik

The classical ?-invariant can be used to determine finiteness properties of kernels of maps onto abelian groups. I will present an analogue invariant that allows us to consider maps onto nilpotent groups instead. A main tool will be partial orders on groups and a possible application is to characterise groups that fibre algebraically. This is based on my doctoral thesis and on ongoing joint work with Sam Fisher.



Angelegt am 30.04.2024 von Anke Pietsch
Geändert am 21.05.2024 von Anke Pietsch
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Oberseminare und sonstige Vorträge
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Heike Harenbrock

Mittagsseminar zur Arithmetik: Pol van Hoften (Amsterdam): Igusa stacks and the cohomology of Shimura varieties

Tuesday, 25.06.2024 10:15 im Raum SRZ 216/217

Mathematik und Informatik

Associated to a modular form f is a two-dimensional Galois representation whose Frobenius eigenvalues can be expressed in terms of the Fourier coefficients of f, using a formula known as the Eichler--Shimura congruence relation. This relation was proved by Eichler--Shimura and Deligne by analyzing the mod p (bad) reduction of the modular curve of level ?0(p). In this talk, I will discuss joint work with Patrick Daniels, Dongryul Kim and Mingjia Zhang, where we give a new proof of this congruence relation that happens "entirely on the generic fibre". More precisely, we prove a compatibility result between the compactly cohomology of Shimura varieties of Hodge type and the Fargues?Scholze semisimple local Langlands correspondence, generalizing the Eichler--Shimura relation of Blasius-Rogawski. Our proof makes crucial use of the Igusa stacks that we construct, generalizing earlier work of Zhang in the PEL case.



Angelegt am 17.06.2024 von Heike Harenbrock
Geändert am 17.06.2024 von Heike Harenbrock
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Oberseminare und sonstige Vorträge
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Vorträge des SFB 1442
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Elke Enning

Ebrahim Samei (Saskatoon): Entropies and Poisson boundaries of probability measures on groups with rapid decay. /
Dietmar Bisch (Vanderbilt University): Graph planar algebra embeddings and new Temperley-Lieb-Jones subfactors. Oberseminar C*-Algebren.

Tuesday, 25.06.2024 16:15 im Raum SRZ 216/217

Mathematik und Informatik

Ebrahim Samei, Saskatoon: Let $G$ be a countable discrete group, and let $\mu$ be a probability measure on $G$ with finite (Shannon) entropy. We initiate the study of several related concepts associate to a probability measure $\mu$ and exploit their relations. First, we look at the concept of {\it Lyapunov exponent} of $\mu$ with respect to weights on $G$ and build a framework that connects it to the entropy of $\mu$ in $G$. This is done by introducing a generalization of Avez entropy, taking into account the given weight, and investigating in details their relations together as well as to the actions of $G$ on measurable stationary spaces. As a byproduct of our techniques, we show that if $G$ has rapid decay w.r.t. a length function $\fL$ and $\mu$ has a finite logarithm moment (w.r.t. $\fL$), the weak containment of the representation $\pi_X$ of $G$ on a $\mu$-stationary space $(X,\xi)$ implies that $$h(G,\mu)=h_\mu(X,\xi),$$ where $h_\mu(X,\xi)$ is the Furstenberg entropy of $(X,\xi)$. This allows us to characterize amenable action of $(G,\mu)$ on stationary spaces: $(X,\xi)$ is an amenable $(G,\mu)$-space if and only if it is a measure-preserving extension of the Poisson boundary of $(G,\mu)$. In particular, if $(X,\xi)$ is a boundary, then $\pi_X$ is weakly contained in $\lambda_G$ if and only if $(X,\xi)$ coincides with the Furstenberg-Poisson boundary of $(G,\mu)$. Hence the action of $G$ on a proper $\mu$-boundary of $G$ is not amenable. This extends the results of Nevo, Zimmer, and others on many hyperbolic like groups. This is a join work with Benjamin Anderson-Sackaney, Tim de Laat, and Matthew Wiersma.

Dietmar Bisch, Vanderbilt University: Since Vaughan Jones introduced the theory of subfactors in 1983, it has been an open problem to determine the set of Jones indices of irreducible, hyperfinite subfactors. Not much is known about this set. Julio Caceres and I have recently shown that all indices of finite depth subfactors between 4 and 5 are realized by new hyperfinite subfactors with Temperley-Lieb-Jones standard invariant as well. They are non-amenable, but have certain nice asymptotic commutativity properties. Our work leads to a conjecture and some results regarding Jones' problem. The construction involves new families of commuting squares, a graph planar algebra embedding theorem, and a few tricks that allow us to avoid solving large systems of linear equations to compute invariants of our subfactors. If there is time, I will mention connections to quantum Fourier analysis and QIT.



Angelegt am 04.04.2024 von Elke Enning
Geändert am 11.06.2024 von Elke Enning
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Oberseminare und sonstige Vorträge
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Stephan Rave

Art Pelling (TU Berlin): Data-driven reduced order modelling for acoustics

Wednesday, 26.06.2024 13:30 im Raum M5

Mathematik und Informatik

The amount of data needed to adequately capture the behaviour of acoustical transmission systems is usually very large. This is not only due to the complex dynamical system behaviour but also the level of fidelity required for keeping up with the human auditory system. For this reason, it has been computationally infeasible to infer realistic state-space models of acoustical systems from data in the past. However, recently, the conjoined use of randomized matrix factorizations and classical system identification methods enabled the construction of large state-space realizations from high-dimensional measurement data. This paves the way for the employment of a plethora of sophisticated model order reduction techniques which in turn sheds new light onto many acoustical modelling challenges. This talk highlights specific challenges of data-driven modelling of acoustical systems. We consider the Eigensystem Realization Algorithm (ERA) and introduce several computational improvements that gear up this classic method for our use case. A validatory application of the method to room impulse response measurements is presented and several applicatory issues are discussed. Finally, an outlook on future research directions and ideas will be given.



Angelegt am 13.03.2024 von Stephan Rave
Geändert am 24.06.2024 von Stephan Rave
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Oberseminar Numerik
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Gabi Dierkes

Jörg Schürmann: The Kirchever construction: From Riemann surfaces to points in the Sato Grassmannian, part II (Research Seminar on Geometry, Algebra and Topology: Moduli Spaces of Complex Curves)

Wednesday, 26.06.2024 16:15 im Raum M3

Mathematik und Informatik



Angelegt am 20.06.2024 von Gabi Dierkes
Geändert am 20.06.2024 von Gabi Dierkes
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Oberseminare und sonstige Vorträge
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Claudia Rüdiger

Dr. Devarshi Mukherjee (Uni Münster): Overconvergent rings and cyclic homology

Wednesday, 26.06.2024 16:30 im Raum M4

Mathematik und Informatik

Abstract: I will use the framework of bornologies to isolate a subcategory of complete "topological" algebras on which K-theory and its tracial approximations have good properties from the viewpoint of noncommutative geometry. These algebras analogous to Scholze-Clausen's recent definition of bounded (commutative) rings in the condensed setup. In the non-archimedean setting, these algebras allow for a functorial definition and a noncommutative version of rigid cohomology. Parts of this project are based on joint work with Ralf Meyer and Guillermo Cortiñas.



Angelegt am 17.06.2024 von Claudia Rüdiger
Geändert am 17.06.2024 von Claudia Rüdiger
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Oberseminare und sonstige Vorträge
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Claudia Rüdiger

Mathias Stout (KU Leuven): Tameness for ordered fields with real analytic structure

Thursday, 27.06.2024 11:00 im Raum SR 4

Mathematik und Informatik

Abstract: It is well-known that the subanalytic structure on the real numbers is o-minimal. Cluckers and Lipshitz have shown that this remains true for elementary extensions of the reals equipped with certain nonstandard analytic functions. More precisely, if B is a real Weierstrass system, then any real closed field with B-analytic structure is o-minimal. In this talk, we consider B-analytic structure on ordered fields that are not necessarily real closed. Such structures cannot be o-minimal in general. Still, they turn out to be tame as valued fields: when equipped with a convex valuation, they give rise to new examples of ?-h-minimal structures. This talk is based on joint work with Kien Huu Nguyen and Floris Vermeulen.



Angelegt am 20.06.2024 von Claudia Rüdiger
Geändert am 20.06.2024 von Claudia Rüdiger
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Oberseminare und sonstige Vorträge
Sonstige Vorträge
Vorträge des SFB 1442
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