12
Fachbereich
Institut für Mathematik
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Oberseminar Geometrische Analysis​​

 

Aug 26 2025
14:00

Mouhammed Moustapha Fall (Mbour/Senegal): tba

Geometrische Analysis

Jul 22 2025
14:00

Leo Brauner (Frankfurt): The mixed Christoffel-Minkowski problem

In this talk, I will first define mixed area measures: these are fundamental geometric measures encoding joint information about curvature of a family of convex bodies (including also the classical Gauss and mean curvature). Then we discuss the central Minkowski and Christoffel problem, as well as their intermediate and mixed versions, which are about classifying mixed area measures. In the special case where the convex bodies involved share an axial symmetry, we resolve the problem completely.
This is joint work with Georg C. Hofstätter and Oscar Ortega-Moreno

Geometrische Analysis

Jul 15 2025
14:00

Esther Cabezas Rivas (Universitat Valencia/Spanien): How to define an inverse mean curvature flow coming out of crystals?


We will start by recalling some basics about smooth versus weak solutions of inverse mean curvature flow (IMCF) from the classical works by Huisken and Ilmanen, where the level set solutions are applied to prove the Riemannian Penrose inequality. But this notion of weak solutions cannot work in milder regularity settings, like those needed to model crystal growth, which require an anisotropic framework (with no regularity nor ellipticity extra requirements), and where the objects to evolve are at most Lipschitz regular. In this a priori unfriendlier scenario, during the second part of the talk, we will explain how we still manage to find a good notion of weak IMCF coming out of a crystal. This is based on joint works with Salvador Moll and Marcos Solera.

 

Jul 8 2025
14:00

Damien Galant (Universität Mons): On the notion of ground state for nonlinear Schrödinger equations on metric graphs

 

Jul 1 2025
14:00

Martín Reiris-Ithurralde (Montevideo/Uruguay)

Geometrische Analysis

Jun 24 2025
14:00

​Nathalie Rieger (Yale University)  Where Time Begins: Geometry at the Origin of the Universe

The Hartle-Hawking "no-boundary" proposal redefines spacetime byoffering
a new way of thinking about the origin of the universe. In math-
ematical terms, it involves manifolds with changing signature type, where
a Riemannian region transitions smoothly into a Lorentzian one at a hy-
persurface marking the onset of time.
Motivated by the "no-boundary" proposal, I present a segment of a
new framework for signature-type changing manifolds, characterized by
a degenerate yet smooth metric. I extend certain tools and results from
Lorentzian geometry to this context, introducing new definitions with
unexpected causal implications. Notably, one such consequence is the
emergence of time-reversing loops through every point on the signature-
change locus.

Geometrische Analysis

Jun 10 2025
14:00

Thomas Mettler (FernUni Schweiz): Flat extensions of principal connections and the Chern-Simons 3-form

I will introduce the notion of a flat extension of a connection on a principal bundle. Roughly speaking, a connection admits a flat extension if it arises as the pull-back of a component of a Maurer–Cartan form. For trivial bundles over closed oriented 3-manifolds, I will relate the existence of certain flat extensions to the vanishing of the Chern–Simons invariant associated to the connection. Joint work with Andreas Cap & Keegan Flood.

Geometrische Analysis

Jun 3 2025
14:00

​Alex Mramor (Universität Kopenhagen): On the singularities of the mean curvature flow under an entropy condition

In this talk I'll introduce Colding and Minicozzi's entropy, discuss the extension of the mean curvature flow with surgery under an entropy bound and discuss how this can be applied to study self shrinkers which are basic singularity models of the flow.


Geometrische Analysis

Mai 27 2025
14:00

Giacomo Di Paolo (Frankfurt): The sufficient condition for solving the Yamabe problem

This talk is based on my Master’s Thesis work in Bologna, under the supervision of Prof. Vittorio Martino. We shall discuss the proof of what we have referred to as the "Resolution Criterion" for the Yamabe problem — namely, the proof by Trudinger and Aubin that the Yamabe problem admits a solution on any manifold whose Yamabe invariant is strictly less than that of the standard sphere. Furthermore, we shall discuss additional aspects of the problem in the case of the standard sphere itself, related to the uniqueness of the solution in this specific setting.

Geometrische Analysis

Mai 20 2025
14:00

Sasa Lukic (RWTH Aachen): Relaxation of perturbed circles in flat spaces for the Mullins-Sekerka evolution in two dimensions

  • The (two-phase) Mullins-Sekerka (MS) model is a free boundary problem arising in various physical contexts such as phase separation and coarsening. It was originally introduced in the context of crystallization processes. In this talk, we discuss the convergence of a perturbed circular interface for the two-phase Mullins-Sekerka evolution in flat two-dimensional space. Our method is based on the gradient flow structure of the evolution and captures two distinct regimes of the dynamics, an initial - and novel - phase of algebraic-in-time decay and a later - and previously explored - phase of exponential-in-time decay. In the first part of the talk, we review the Mullins-Sekerka flow, contrast it with other well-known curvature flows such as the curve shortening flow and examine its gradient flow structure. Then, we briefly discuss prior results in the literature, our result and the main proof ideas in the second part. In the third and final part, the focus will be on a few key techniques employed in the proof.