Geometric Analysis Seminar

Organizers: Miles Simon and Jiawei Liu

Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, Germany.

Seminars are usually held on Thursday, 15:00-16:00.

Currently, the seminar is held online on Zoom. Please contact the organizers to be added to the mailing list and receive the Zoom link and password.

Spring 2021

Thursday, April 8, 15:00-16:00, Zoom Meeting

Alix Deruelle (Institut de mathématiques de Jussieu-Paris Rive Gauche)

Title: A relative entropy for expanders of the Ricci flow

Abstract: Expanding self-similar solutions of the Ricci flow are solutions which evolves by scaling and diffeomorphisms only. Such solutions are also called expanding gradient Ricci solitons. These "canonical" metrics are potential candidates for smoothing out isolated singularities instantaneously. These heuristics apply to the Kähler-Ricci flow too. In this talk, we ask the question of uniqueness of such self-similar solutions coming out of a given metric cone over a smooth link. As a first step, we make sense of a suitable Lyapunov functional also called relative entropy in this setting.

Thursday, April 15, 15:00-16:00, Zoom Meeting, Upcoming

Man-Chun Lee (Northwestern University and University of Warwick)

Title: d_p convergence and epsilon-regularity theorems for entropy and scalar curvature lower bound

Abstract: In this talk, we consider Riemannian manifolds with almost non-negative scalar curvature and Perelman entropy. We establish an epsilon-regularity theorem showing that such a space must be close to Euclidean space in a suitable sense. We will illustrate examples showing that the result is false with respect to the Gromov-Hausdorff and Intrinsic Flat distances, and more generally the metric space structure is not controlled under entropy and scalar lower bounds. We will introduce the notion of the d_p distance between (in particular) Riemannian manifolds, which measures the distance between W^{1,p} Sobolev spaces, and it is with respect to this distance that the epsilon regularity theorem holds. This is joint work with A. Naber and R. Neumayer.

Thursday, May 6, 15:00-16:00, Zoom Meeting

Tobias Marxen (Carl von Ossietzky Universität Oldenburg)



Thursday, May 20, 15:00-16:00, Zoom Meeting

Klaus Kröncke (Universität Hamburg)



Thursday, May 27, 15:00-16:00, Zoom Meeting

Oliver Lindblad Petersen (Stanford University)



Thursday, June 17, 15:00-16:00, Zoom Meeting

Felix Schulze (University of Warwick)