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Sandra Huppert

Oberseminar Differentialgeometrie: Artemis Vogiatzi (University of London), Vortrag: High Codimension Mean Curvature Flow in $mathbb{C}P^n$.

Monday, 15.04.2024 16:00 im Raum SRZ 214

Mathematik und Informatik

Abstract: Mean curvature flow is a geometric evolution equation that describes how a submanifold embedded in a higher-dimensional space changes its shape over time. We establish a codimension estimate that enables us to prove at a singular time of the flow, there exists a rescaling that converges to a smooth codimension one limiting flow in Euclidean space, regardless of the original flow's codimension. Under a cylindrical type pinching, we show that this limiting flow is weakly convex and either moves by translation or is a self-shrinker. These estimates allow us to analyse the behaviour of the flow near singularities and establish the existence of the limiting flow. Considering the $\mathbb{C}P^n$, we go beyond the finite timeframe of the mean curvature flow, by proving that the rescaling converges smoothly to a totally geodesic limit in infinite time. Our approach relies on the preservation of the quadratic pinching condition along the flow and a gradient estimate that controls the mean curvature in regions of high curvature.



Angelegt am Thursday, 07.03.2024 10:39 von Sandra Huppert
Geändert am Monday, 11.03.2024 08:27 von Sandra Huppert
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Heike Harenbrock

Oberseminar p-adische Arithmetik: Analytic stacks: Claudius Heyer: Light condensed abelian groups and their cohomology

Monday, 15.04.2024 12:15 im Raum SRZ 216/217

Mathematik und Informatik



Angelegt am Thursday, 11.04.2024 09:39 von Heike Harenbrock
Geändert am Thursday, 11.04.2024 09:39 von Heike Harenbrock
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Claudia Rüdiger

Rune Haugseng (Norwegian University of Science and Technology): Equivariant ring spectra and homotopical Tambara functors

Wednesday, 10.04.2024 14:00 im Raum M6

Mathematik und Informatik

Abstract: A Tambara functor is ring-like structure, where in addition to addition and multiplication we have both additive and multiplicative norms (or transfers) for subgroups of a given finite group G; more formally, they can be defined as certain product-preserving functors out of a (2,1)-category of bispans of finite G-sets. Tambara functors often show up as equivariant analogues of commutative rings - for example, the 0th homotopy group of a genuine commutative equivariant ring spectrum is a Tambara functor. In this talk I will discuss a description of the ?-category of connective commutative equivariant ring spectra as Tambara functors valued in ?-groupoids; this is joint work in progress with Bastiaan Cnossen, Tobias Lenz, and Sil Linskens.



Angelegt am Monday, 08.04.2024 06:13 von Claudia Rüdiger
Geändert am Monday, 08.04.2024 06:13 von Claudia Rüdiger
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Sandra Huppert

Oberseminar Differentialgeometrie: Stephan Stadler (MPI Bonn), Vortrag: Rigidity of ideal symmetric sets

Monday, 22.04.2024 16:00 im Raum SRZ 214

Mathematik und Informatik

Abstract: A subset in the ideal boundary of a CAT(0) space is called symmetric if every complete geodesic with one ideal boundary point in the set has both ideal boundary points in the set. In the late 80s Eberlein proved that if a Hadamard manifold contains a non-trivial closed symmetric subset in its ideal boundary, then its holonomy group cannot act transitively. This leads to rigidty via the Berger-Simons Theorem. I will discuss rigidity of ideal symmetric sets in the general context of locally compact geodesically complete CAT(0) spaces.



Angelegt am Thursday, 07.03.2024 10:41 von Sandra Huppert
Geändert am Monday, 25.03.2024 07:57 von Sandra Huppert
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Heike Harenbrock

Mittagsseminar zur Arithmetik: Felix Schremmer (Hong Kong): Beyond minute admissible sets

Tuesday, 23.04.2024 10:15 im Raum SRZ 216/217

Mathematik und Informatik

If a Shimura variety is fully Hodge-Newton decomposable, its mod p reduction enjoys particularly nice properties. These cases are well-understood and characterized by a certain inequality known as the minute condition. In a joint project with Xuhua He and Eva Viehmann, we study the next larger cases, where the minute condition is barely not satisfied any more. I will give a classification of these cases and explain the geometric properties of the corresponding Ekedahl-Oort and Kottwitz-Rapoport strata. The Ekedahl-Oort strata are described by a new class of affine Deligne-Lusztig varieties introduced in a joint work with Ryosuke Shimada and Qingchao Yu. For these affine Deligne-Lusztig varieties of positive Coxter type, we give a full description of their dimensions and the sets of irreducible components.



Angelegt am Monday, 08.04.2024 10:06 von Heike Harenbrock
Geändert am Monday, 08.04.2024 10:06 von Heike Harenbrock
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Claudia Rüdiger

Alexis Aumonier (University of Cambridge): Stable cohomology of moduli of smooth hypersurfaces

Wednesday, 24.04.2024 16:30 im Raum M4

Mathematik und Informatik

Abstract: The space of all smooth hypersurfaces of a given degree in a complex projective variety is itself a variety. I will explain how to understand some of its cohomology using tools from homotopy theory: smooth hypersurfaces are given by holomorphic sections of line bundles subject to a differential condition, and these can be compared to continuous sections of appropriate jet bundles. This strategy usually goes under the name of "h-principle", and we will see an algebraic instance of that. I will also explain some consequences: a cohomological stability phenomenon, and a relation to classifying spaces of diffeomorphism groups of hypersurfaces.



Angelegt am Wednesday, 10.04.2024 11:00 von Claudia Rüdiger
Geändert am Wednesday, 10.04.2024 11:00 von Claudia Rüdiger
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Kristina Wensing

Ada Lovelace Seminar

Friday, 26.04.2024 14:00 im Raum SRZ 216/217

Mathematik und Informatik

Research Talks by the Ada Lovelace Fellows 2023



Angelegt am Tuesday, 06.02.2024 10:34 von Kristina Wensing
Geändert am Tuesday, 06.02.2024 10:34 von Kristina Wensing
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