12
Fachbereich
Institut für Mathematik
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Oberseminar Geometrische Analysis​​

Geometrische Analysis

Apr 14 2026
14:00

Ilka  Agricola (Marburg)

Geometrische Analysis

Mär 17 2026
14:00

Raum 903

Giorgio Saracco (Ferrara, Italien)

Geometrische Analysis

Feb 10 2026
14:00

Raum 903

Miles Simon (Magdeburg): tba

Geometrische Analysis

Feb 3 2026
14:00

Raum 903

Mohammad Ivaki (Wien)

Geometrische Analysis

Jan 20 2026
14:00

Raum 903

Thomas Wannerer (Jena): Translation invariant curvature measures of convex bodies 

In a series of papers, Weil initiated the investigation of translation invariant curvature measures of convex bodies, which include as prime examples Federer's curvature measures. In on-going work, we continue this line of research by introducing new tools to study curvature measures. Our main results suggest that the space of curvature measures, which is graded by degree and parity, is highly structured: We conjecture that each graded component has length at most $2$ as a representation of the general linear group, and we prove this in degree $0$ and $n-2$. Beyond this conjectural picture, our methods yield a characterization of Federer's curvature measures under weaker assumptions.

Based in part on joint work with Jakob Schuhmacher. 

Geometrische Analysis

Dez 16 2025
14:00

Raum 903

Shujing Pan (Frankfurt): The quermassintegral inequalities for horo-convex domains in the sphere

In this talk, I will introduces a new notion of convexity on the unit sphere, called horo-convexity, inspired by its analogue in hyperbolic space. For horo-convex hypersurfaces, we prove the smooth convergence of the Guan–Li inverse curvature flow and, as a consequence, establish the full set of quermassintegral inequalities on the sphere. The talk will briefly outline the definition, the flow approach, and the main geometric results. This talk is based on joint work with Julian Scheuer

Geometrische Analysis

Dez 2 2025
14:00

Raum 903

Marcus Flook (Australian National University): Mean curvature flow analogues in Cauchy-Riemann (CR) Geometry

In this talk, I will introduce and motivate Cauchy-Riemann (CR) geometry by considering real hypersurfaces embedded in complex Euclidean space. Firstly, I will discuss progress on both Darboux- and Alexandrov-type theorems in this setting. Secondly, I will introduce flows of CR hypersurfaces that are analogous to the mean curvature flow. Alongside the standard degeneracy due to tangential diffeomorphisms, such flows have an additional degeneracy due to the CR structure which will be discussed. Finally, I will discuss joint research with Ben Andrews on new flows which preserve key components of the CR structure. This talk will be accessible to those with a background in Riemannian geometry.

Geometrische Analysis

Nov 18 2025
14:00

Georg Hofstätter (TU Wien): Localization of valuations and Alesker’s irreducibility theorem

We introduce a new localization technique for translation-invariant valuations on
convex bodies. We then apply it to show that smooth, translation-invariant valua-
tions are representable by integration over the normal cycle. With this representa-
tion, we provide a new proof of Alesker’s famous irreducibility theorem.
This is joint work with J. Knoerr.

Geometrische Analysis

Nov 4 2025
14:00

Tim Laux (Heidelberg): Equivalence of weak solution concepts for mean curvature flow

Abstract:  Mean curvature flow is a fundamental geometric evolution equation with natural applications in almost every field of science. To study the evolution past singularities, several notions of weak solutions have been introduced over the last decades. The viscosity solution on the one hand is based on a geometric comparison principle. On the other hand, many other concepts are variational in nature as they are inspired by the gradient flow structure of mean curvature flow. In this talk, I will show that these two viewpoints are equivalent in the following sense: (i) any generic level set of the viscosity solution is a variational solution; (ii) any foliation by variational solutions has to be equal to the unique viscosity solution. This also implies the generic uniqueness of variational solutions.


Geometrische Analysis

Okt 21 2025
14:00

Nicola De Nitti (Pisa/Italien): Optimal transport of measures via autonomous vector fields

We study the problem of transporting one probability measure to another via an autonomous velocity field. We rely on tools from the theory of optimal transport. In one space-dimension, we solve a linear homogeneous functional equation to construct a suitable autonomous vector field that realizes the (unique) monotone transport map as the time-1 map of its flow. Generically, this vector field can be chosen to be Lipschitz continuous. We then use Sudakov's disintegration approach to deal with the multidimensional case by reducing it to a family of one-dimensional problems. This talk is based on a joint work with Xavier Fernández-Real.