The seminar takes place on Fridays, at 14:15 in SR 2.040.
Mailing List
In order to receive e-mails about the Group seminar, please subscribe to the mailing list or send a short e-mail to sanchez(at)iam.uni-bonn(dot)de (Daniel Sánchez-Simón del Pino)
Upcoming
December 5 at 14:15 in SR 2.040 .
Speaker: Prof. Marvin Weidner
Title: Optimal regularity for kinetic equations in domains
The Boltzmann equation is one of the central equations in statistical mechanics and models the evolution of a gas through particle interactions. In recent years, groundbreaking work by Imbert and Silvestre has led to a conditional regularity theory for periodic solutions of the Boltzmann equation. A major open challenge is whether such a theory can be extended to bounded domains with physically relevant boundary conditions.
As a first step toward understanding the boundary case, in this talk I will discuss the smoothness of solutions to linear kinetic Fokker-Planck equations in domains with specular reflection condition. While the interior regularity of such equations is well understood, their behavior near the boundary has remained open, even in the simplest case of Kolmogorov's equation. I will also mention recent results on other boundary conditions such as diffuse reflection and in-flow.
This talk is based on joint works with Xavier Ros-Oton and Kyeongbae Kim.
Schedule
October 17
Francesca Pieroni
October 24
No seminar
October 31
No seminar
November 7
Elena Demattè (¡Thesis defense! :))
November 14
Sebastián Flores Sepúlveda
November 21
TBA
November 28
TBA
December 05
Prof. Marvin Weidner
December 12
No seminar
December 19
TBA
December 26
No seminar
January 9
Dr. Irina Aleksandrova
January 16
Dr. Eugenia Franco
January 23
No seminar
January 30
TBA
Past talks
October 17 at 14:15 in SR 2.040 .
Speaker: Francesca Pieroni (Sapienza Università di Roma)
Title: Random Euclidean Matching for exponentially decaying densities
The Random Euclidean Matching problem is the problem of finding the optimal matching between two families of iid random variables distributed in a d-dimensional domain. Here "optimal" refers to the cost function determined by the sum of the distances between couples of points (elevated to a power p).
In this talk we will first focus on the matching of variables distributed on bounded connected domains. Then we will investigate the case of iid random variables distributed in $\mathbb{R}^d$ according to an exponentially decaying probability density.
November 14 at 14:15 in SR 2.040 .
Speaker: Sebastián Flores Sepúlveda
Title: The moving patch model with fractional Laplacian
In this talk we will discuss a one-dimensional reaction-diffusion equation driven by the fractional Laplacian, given by $u_t + (-\Delta)^s u = f(x-ct, u)$ with $c\in \mathbb{R}$ is a constant. This equation arises as a model for a species subject to a moving environment. We will explain the relation between the long-time behavior of solutions to the parabolic problem, the existence of nontrivial traveling waves and the sign of some generalized principal eigenvalue for an elliptic operator, and detail the main differences between the cases of the fractional and the classical Laplacian.
