Seminars Archive

Oberseminar Analysis-Probability


DateLink to Abstract
21.09.2022Speaker and Abstract
Speaker and Abstract
20.09.2022Speaker and Abstract
13.09.2022Speaker and Abstract
06.09.2022Speaker and Abstract
02.08.2022Speaker and Abstract
19.07.2022Speaker and Abstract
Speaker and Abstract
Speaker and Abstract
13.05.2022Speaker and Abstract
15.03.2022Speaker and Abstract
08.03.2022Speaker and Abstract
01.03.2022Speaker and Abstract
16.02.2022Speaker and Abstract
01.02.2022Speaker and Abstract
31.01.2022Speaker and Abstract
25.01.2022Speaker and Abstract


DateLink to Abstract
09.11.2021Speaker and Abstract
21.09.2021Speaker and Abstract
14.09.2021Speaker and Abstract
24.08.2021Speaker and Abstract
01.06.2021Speaker and Abstract
11.05.2021Speaker and Abstract
27.04.2021Speaker and Abstract
20.04.2021Speaker and Abstract
13.04.2021Speaker and Abstract
19.01.2021Speaker and Abstract

Oberseminar Probability and variational methods in PDEs

Wintersemester 2021/22

DateSpeaker and Title
09.12.2021Daniel Heydecker (MPI for Mathematics in the Sciences Leipzig)
Large Deviations of Kac’s Random Walk
Kac introduced a many-particle Markov process, corresponding to the spatially homogeneous Boltzmann equation, and we consider the dynamical large deviations in the limit [latex]N\to\infty[/latex]. With the expected rate function, the large deviations lower bound is only true on a restricted class of paths, and we find counterexamples to a global lower bound related to Lu and Wennberg’s energy non-conserving solutions to the Boltzmann equation. On the other hand, the class of paths where we have a matching upper and lower bounds is sufficiently rich to rederive the celebrated Boltzmann H-Theorem.
11.01.2022Angkana Rüland (Heidelberg University)
On Scaling Laws for Some Matrix-Valued m-Well Problems
Highly non-(quasi)-convex, matrix-valued differential inclusions arise in numerous physical applications. One such example is the modelling of shape-memory alloys. In these settings, often the exact differential inclusions display a striking dichotomy between rigidity and flexibility in that
– solutions of sufficiently high regularity obey the “characteristic equations” determined by the differential inclusion, the solutions are rigid in this sense, – while low regularity solutions are highly non-unique and hence extremely flexible.
In order to investigate this dichotomy further, in this talk, I explore the effects of regularizations in the form of singular perturbation problems with vanishing regularization strength for these differential inclusions. Motivated by applications in shape-memory alloys, I discuss the role of scaling properties in the singular perturbation strength. In particular, I study two prototypical types of differential inclusions and illustrate how the structure of the underlying convex hulls results in the presented scaling laws. This is based on joint work with Jamie Taylor,  Antonio Tribuzio, Christian Zillinger and Barbara Zwicknagl.
24.02.2022Georgiana Chatzigeorgiou (MPI for Mathematics in the Sciences Leipzig)
On the theory of fluctuations in stochastic homogenization 
This talk focuses on stochastic homogenization for linear elliptic equations in divergence form. In particular, we study weakly correlated Gaussian environments and emphasize on the recently developed theory of fluctuations. More precisely, it has been observed that the fluctuations of averages of the solution are captured by the so-called standard homogenization commutator Ξ, an object given in terms of the homogenization correctors. This suggests that a more delicate analysis of Ξ is needed. Our aim is to explain how Ξ decorrelates on large scales when it is averaged on balls which are far enough. We give a quantitative characterization of this decorrelation in terms of both the macroscopic scale and the distance between the balls showing that Ξ inherits the locality properties of the environment.
07.03.2022Florian Kunick (MPI for Mathematics in the Sciences Leipzig)
Thermodynamically consistent and positivity-preserving discretization of the thin-film equation with thermal noise
It is known that the thin-film equation has a gradient flow structure with respect to a (generalized) Wasserstein metric and the usual Dirichlet energy. Based on that, the fluctuation-dissipation theorem gives rise to a stochastic thin-film equation. This equation is a singular stochastic partial differential equation which is out of scope of the framework of regularity structures for now. In order to circumvent this issue, we discretize the gradient flow structure and rediscover a well-known discretization of the (deterministic) thin-film equation that preserves the so-called entropy estimate. In the stochastic setting this entropy estimate then yields positivity for the solution in the case that the mobility arises from the no-slip boundary condition. Moreover, we show that previous discretizations of the stochastic thin-film equation considered in the literature do not preserve positivity. This is joint work with Benjamin Gess, Rishabh Gvalani and Felix Otto.

Oberseminar Calculus of Variations and Applications

Please see the seminar website at LMU Munich for more details.