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Events
n Cities seminar

MPI für Mathematik in den Naturwissenschaften Leipzig

E1 05 (Leibniz-Saal)

conference

03/05/2024 03/05/2024

n Cities seminar

The n cities seminar is organized by mathematicians from the universities of Chemnitz, Dresden, Freiberg, Halle and Leipzig, as well as the Max Planck Institute for Mathematics in the Sciences (MiS) in Leipzig (currently by Swanhild Bernstein, Ralph Chill, Thomas Kalmes, Felix Otto, Felix Pogorzelski and Nils Waterstraat) and is dedicated, but not restricted to a variety of fields in a neighborhood of analysis, amongst them:

Functional analysis
Analysis of partial differential equations
Complex analysis
Operator theory
Theory of operator semigroups
Probability and ergodic theory

Speakers

Nora Doll

Martin-Luther-Universität Halle-Wittenberg

Jonas Hirsch

Universität Leipzig

Jonas Miehe

Technische Universität Chemnitz

Peter Morfe

MPI MiS

Marianna Porfido

TU Bergakademie Freiberg

Claudia Raithel

TU Dresden

Program

12:45 - 13:30	Jonas Miehe (Technische Universität Chemnitz) Fermionic integration and perturbations of semigroups In this talk I will explain an algebraic machinery, based on Fermionic integration, which basically allows to rewrite expressions of the form \begin{equation} \int_{t \sigma_n} e^{-s_1 H} P_1 e^{-(s_2 - s_1)H} P_2 \dots e^{-(s_n - s_{n-1})H}P_n e^{-(t - s_n)H} \, \mathrm{d}s_1 \ldots \mathrm{d}s_n, \quad t \geq 0, \end{equation} as analytic semigroups. Here, $H \geq 0$ is an unbounded self-adjoint operator and each $P_j$ is an unbounded possibly non-self-adjoint operator. Applications to noncommutative geometry will be presented. This is joint work with Batu Güneysu.
13:30 - 14:15	Claudia Raithel (TU Dresden) Density fluctuations in weakly interacting particle systems via the Dean-Kawasaki equation It has been proposed that the density fluctuations of a system of weakly interacting particles in the regime of large but finite particle number are captured by a highly singular SPDE -the Dean-Kawasaki equation. Due to the ever expanding use of the Dean-Kawasaki equation in applications, there is a desire to rigorously justify it. In this talk we show that, using a suitable weak distance, the law of the fluctuations as predicted by a spatially discretized Dean-Kawasaki equation approximates the law of the fluctuations of the particle system up to a term that is of arbitrary order in the inverse particle number and a numerical error. This talk is based on a joint work with Federico Cornalba, Julian Fischer, and Jonas Ingmanns.
14:15 - 15:00	Marianna Porfido (TU Bergakademie Freiberg) Kernel estimates for a class of fractional Kolmogorov operators In this talk I will present some recent results obtained in [1]. We consider a measure space $(X,\mu)$ with $\sigma$-finite measure $\mu$ and a non-negative self-adjoint operator $A$ on $L^2(\mu)$. We assume that $-A$ generates a symmetric Markov semigroup on $L^2(\mu)$, namely a symmetric positivity preserving and $L^\infty$-contractive strongly continuous semigroup on $L^2(\mu)$.We prove non-uniform bounds on the transition kernel corresponding to the Markov semigroup generated by $-A^\alpha$ for $0
15:00 - 15:30	Coffee Break
15:30 - 16:15	Nora Doll (Martin-Luther-Universität Halle-Wittenberg) Orientation flow for real skew-adjoint Fredholm operators with odd-dimensional kernel The orientation flow of paths of bounded real skew-adjoint Fredholm operators with invertible endpoints was studied by Carey, Phillips and Schulz-Baldes. In this talk, an orientation flow of norm-continuous paths of bounded real skew-adjoint Fredholm operators with odd-dimensional kernel is introduced and studied. This orientation flow is defined with respect to a real one-dimensional reference projection. It is homotopy invariant and fulfills a concatenation property. When applied to closed paths it is independent of the reference projection and provides an isomorphism of the fundamental group of the space of bounded real skew-adjoint Fredholm operators with odd-dimensional kernel, equipped with the norm topology, to Z2.
16:15 - 17:00	Jonas Hirsch (Universität Leipzig) On the Lawson-Osserman conjecture on the minimal surfaces system Please see the abstract as PDF file below. Abstract
17:00 - 17:45	Peter Morfe (MPI MiS, Leipzig) Minimal Lipschitz Extensions and the Finsler Infinity Laplacian The minimal Lipschitz extension problem is the prototypical example of an L^{\infty} variational problem, the study of which was initiated by Aronsson in the 1960's. When the Lipschitz seminorm under consideration is defined relative to the Euclidean norm, a well-developed theory shows that so-called absolutely minimizing Lipschitz extensions are characterized by the infinity Laplace equation, an L^{\infty} version of the classical Laplace equation. In 2004, Aronsson, Crandall, and Juutinen observed that, when the Euclidean norm is replaced by an arbitrary (Finsler) norm, absolutely minimizing Lipschitz extensions solve a PDE involving a potentially very complicated, discontinuous elliptic operator, the Finsler infinity Laplace equation. Since then, proving absolute minimality of solutions of this and related PDE has been an important question in the L^{\infty} calculus of variations. In this talk, I discuss recent work establishing that the Finsler infinity Laplace equation does, in fact, characterize absolutely minimizing Lipschitz extensions.
18:30 - 00:00	Dinner at Barthels Hof

Participants

Bernhard Aigner

TU Bergakademie Freiberg

Swanhild Bernstein

TU Bergakademie Freiberg

Tomas Dohnal

MLU Halle-Wittenberg

Elias Döhrer

TU Chemnitz

Nora Doll

Martin-Luther-Universität Halle-Wittenberg

Uta Renata Freiberg

TU Chemnitz

Maximilian Hanisch

Martin-Luther University Halle

Jan Hausmann

TU Dresden

RUNAN HE

Martin-Luther-Universität Halle-Wittenberg

Jonas Hirsch

Universität Leipzig

Thomas Kalmes

TU Chemnitz

Meugang Toukam Kevine

MPI MiS

Lukas Koch

MPI MiS

Jonas Miehe

Technische Universität Chemnitz

Peter Morfe

MPI MiS

Fenna Müller

Universität Leipzig

Stefan Neukamm

TU Dresden

Felix Otto

Max Planck Institute for Mathematics in the Sciences

Dirk Pauly

TU Dresden

Felix Pogorzelski

Universität Leipzig

Marianna Porfido

TU Bergakademie Freiberg

Claudia Raithel

TU Dresden

Philipp Reiter

Chemnitz University of Technology

Kai Richter

TU Dresden

Michael Schomburg

TU Dresden

Akram Sharif

TU Dresden

Nathanael Skrepek

TU Freiberg

Janko Stennder

TU Dresden

Christian Wagner

MPI MIS

Nils Waterstraat

MLU Halle-Wittenberg

Mathias Wilke

MLU Halle-Wittenberg

Martha Zimmermann

TU Bergakademie Freiberg

Scientific Organizers

Felix Otto

Max Planck Institute for Mathematics in the Sciences

Felix Pogorzelski

Universität Leipzig

Administrative Contact

Katja Heid

Max Planck Institute for Mathematics in the Sciences Contact via Mail

n Cities seminar

Links

Speakers

Nora Doll

Jonas Hirsch

Jonas Miehe

Peter Morfe

Marianna Porfido

Claudia Raithel

Program

Participants

Bernhard Aigner

Swanhild Bernstein

Tomas Dohnal

Elias Döhrer

Nora Doll

Uta Renata Freiberg

Maximilian Hanisch

Jan Hausmann

RUNAN HE

Jonas Hirsch

Thomas Kalmes

Meugang Toukam Kevine

Lukas Koch

Jonas Miehe

Peter Morfe

Fenna Müller

Stefan Neukamm

Felix Otto

Dirk Pauly

Felix Pogorzelski

Marianna Porfido

Claudia Raithel

Philipp Reiter

Kai Richter

Michael Schomburg

Akram Sharif

Nathanael Skrepek

Janko Stennder

Christian Wagner

Nils Waterstraat

Mathias Wilke

Martha Zimmermann

Scientific Organizers

Felix Otto

Felix Pogorzelski

Administrative Contact

Katja Heid