Fachbereich Mathematik

# Vorträge in der Woche 28.11.2022 bis 04.12.2022

Vorherige Woche Nächste Woche Alle Vorträge

## Jonas Hetz (Stuttgart)

An important task in the representation theory of finite groups is the determination of their character tables. As the classification of finite simple groups shows, the main difficulties in this context concern the finite groups of Lie type, which arise as an infinite series of finite groups associated to a certain algebraic group over a field of positive characteristic. In order to generically tackle the problem of determining the character tables of finite groups of Lie type, Lusztig developed the theory of character sheaves in the 1980s. In this framework, due to the work of Lusztig and Shoji, the problem is in principle reduced to determining certain roots of unity. We report on some recent progress in this area.

 Uhrzeit: 14:00 - 15:00 Ort: C4H33 Gruppe: Oberseminar kombinatorische algebraische Geometrie Einladender: Daniele Agostini, Hannah Markwig

## Prof. Dr. Victor Batyrev (Universität Tübingen)

Wir definieren zu jedem $d$-dimensionalen Gitterpolytop $P$ eine Höhenfunktion $h_P$ auf der Menge $T({\bf Q})$ von rationalen Punkten eines $d$-dimensionalen algebraischen Torus $T$. Für jede positive reelle Zahl $B$ wird die Anzahl $N(P,B)$ der Punkte $x \in T({\bf Q})$ der Höhe $h_P(x) < B$ endlich. Unser Ziel ist es, das asymptotische Verhalten der Zahl $N(P,B)$ für $B \to \infty$ kombinatorisch durch das Gitterpolytop $P$ zu bestimmen.

 Uhrzeit: 14:00 Ort: Hörsaalzentrum N2 Gruppe: Oberseminar Algebraische Geometrie Einladender: V. Batyrev, J. Hausen, Th. Markwig

## Andreas Prohl (Universität Tübingen)

In the talk, I survey numerical methods to approximate the solution of the linear wave equation driven by noise. I discuss a new method which is of order 2/3, and complement the theory with computational studies.

 Uhrzeit: 14:15 Ort: 1B01, Hörsaalzentrum Gruppe: Oberseminar Numerik Einladender: Lubich, Prohl

## Andoni Royo Abrego

Ancient solutions of geometric flows such as Ricci flow and Mean curvature flow arise naturally as models for singularity formation. There has been significant progress towards the classification of such solutions under natural geometric assumptions. In this seminar I will survey some of these results for the Ricci flow as well as discuss a dimension reduction procedure for ancient solutions with optimal curvature growth. This leads to further classification results in higher dimensions.

 Uhrzeit: 14:15 Ort: S9 (C06H05) Den Zoom-Link erhalten Sie per E-Mail von Frau Martina Jung oder Frau Martina Neu. For participating online, please sign up by sending an email to Martina Jung or Martina Neu. Gruppe: Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie Einladender: Carla Cederbaum, Melanie Graf, Gerhard Huisken, zusammen mit Jan Metzger (Potsdam)

## Matilde Manzaroli

In a work in progress with Emiliano Ambrosi, we study the real topology of totally real semistable degenerations, with certain technical conditions on the special fiber X0, and we give a bound for the individual real Betti numbers of a smooth fiber near 0 in terms of the complex geometry of X0. The main ingredient is the use of real logarithmic geometry, which allows to work with degenerations which are not necessarily toric and hence to go beyond the case of tropically smooth degenerations. This, in particular, generalises previous work of Renaudineau-Shaw, obtained via tropical techniques, to a more general setting.

 Uhrzeit: 15:30 - 16:30 Ort: C4H33 Gruppe: Oberseminar kombinatorische algebraische Geometrie Einladender: Daniele Agostini, Hannah Markwig

## Dr. Elena Giorgi (Columbia University)

Most works on the analysis of the wave equation on Kerr black holes rely on a combination of the vector field method and Fourier decomposition, with the notable exception of a generalized vector field method introduced by Andersson-Blue. Their method allows for commutation with second order differential operators entirely in physical-space by supplementing the Killing vector fields with the Carter operator of Kerr to obtain a local energy decay identity at the level of three derivatives of the solution for sufficiently small |a|. I this talk I will describe the main ideas of Andersson-Blue’s method and explain its advantages in two recent applications where physical space-estimates have been crucial: the linear stability of Kerr-Newman black hole to coupled gravitational-electromagnetic perturbations and our proof of the non-linear stability of the slowly rotating Kerr family with Klainerman-Szeftel.

 Uhrzeit: 15:30 Ort: online - wenn Sie Zugang haben wollen, schicken Sie bitte eine Nachricht an Martina Jung Gruppe: Oberseminar Einladender: Carla Cederbaum