Patrick Ghanaat (UniFr)
Almost flat manifolds abstract
Abstract:
This expository talk will be centered on one of the classical “pinching”theorems of Riemannian geometry, due to Gromov in its original form:Compact connected manifolds admitting a Riemannian metric with suitably small curvature are diffeomorphic to infra-nilmanifolds.Flat Riemannian manifolds are quotients Λ\\Rn of euclidean Rn bya discrete group Λ of isometries. More generally, infra-nilmanifolds arequotients Λ\\N of a nilpotent Lie group by a discrete group Λ of isome-tries of a left invariant Riemannian metric on N .We will begin with background on nilpotent Lie groups, their metrics,isometries and quotients, then explain the history and versions of thetheorem, outline a proof following ideas of Auslander, and discuss someclosely related questions.
10:20 • Université de Fribourg, room Phys 2.52
Mirko Mauri (Ecole Polytechnique)
Title T.B.A.
13:15 • EPF Lausanne, CM 1 517
Dr. Homin Lee (Northwestern University)
Title T.B.A.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Prof. Dr. Francois Greer (Michigan State University)
Title T.B.A.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Riccardo Tione (MPI Leipzig)
Abstract:
This talk concerns critical points $u$ of polyconvex energies of the form $f(X) = g(det(X))$, where $g$ is (uniformly) convex. It is not hard to see that, if $u$ is smooth, then $\\det(Du)$ is constant. I will show that the same result holds for Lipschitz critical points $u$ in the plane. I will also discuss how to obtain rigidity for approximate solutions. This is a joint work with A. Guerra.
14:15 • Universität Basel, Spiegelgasse 5, Seminarraum 05.002
Min Jun Jo (Duke University)
Abstract:
TBA
15:15 • Universität Basel, Spiegelgasse 5, Seminarraum 05.002
Alexandra Kjuchukova (University of Notre Dame)
Title T.B.A.
15:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Gilles Vilmart (Uni Geneva)
Langevin dynamics with fast perturbation driven by Stratonovich noise for enhancing probability measure sampling abstract
Abstract:
We propose a perturbation of Langevin dynamics for enhancing the sampling from probability measures in, possibly, high dimensional spaces. Precisely, by perturbing Langevin dynamics by a suitable Stratonovich noise that preserves the invariant measure of the original system, we show that accelerated convergence to equilibrium and reduced asymptotic variance can be achieved.This talk is based on joint work with A. Abdulle† and G. A. Pavliotis (Imperial College London).
16:00 • EPF Lausanne, Bernoulli Center
Dr. Leonardo Zepeda-Nunez (Google Research, USA)
Recent Advances in Probabilistic Scientific Machine learning abstract
Abstract:
The advent of generative AI has turbocharged the development of a myriad of commercial applications, and it has slowly started to permeate to scientific computing. In this talk we discussed how recasting the formulation of old and new problems within a probabilistic approach opens the door to leverage and tailor state-of-the-art generative AI tools. As such, we review recent advancements in Probabilistic SciML – including computational fluid dynamics, inverse problems, and particularly climate sciences, with an emphasis on statistical downscaling.Statistical downscaling is a crucial tool for analyzing the regional effects of climate change under different climate models: it seeks to transform low-resolution data from a (potentially biased) coarse-grained numerical scheme (which is computationally inexpensive) into high-resolution data consistent with high-fidelity models.We recast this problem in a two-stage probabilistic framework using unpaired data by combining two transformations: a debiasing step performed by an optimal transport map, followed by an upsampling step achieved through a probabilistic conditional diffusion model. Our approach characterizes conditional distribution without requiring paired data and faithfully recovers relevant physical statistics, even from biased samples.We will show that our method generates statistically correct high-resolution outputs from low-resolution ones, for different chaotic systems, including well known climate models and weather data. We show that the framework is able to upsample resolutions by 8x and 16x while accurately matching the statistics of physical quantities – even when the low-frequency content of the inputs and outputs differs. This is a crucial yet challenging requirement that existing state-of-the-art methods usually struggle with.
16:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room E 1.2
Dr. Geronimo Uribe Bravo (Universidad Nacional Autónoma de México)
A pathwise approach to time change abstract
Abstract:
Time-change equations are a generalization of ordinary differentialequations which are driven by the random, irregular, and possibly denselydiscontinuous sample paths of the typical stochastic process. They can be thought of as a multiparameter version of the methodof time-change and can be given a pathwise theory. Time-change equations can lead to deep results on weak existence anduniqueness of stochastic differential equations and posses a robuststrong approximation theory. However, time-change equations are notrestricted to Markovian or semimartingale settings. In this talk, we will go through some examples of time-changeequations which can be succesfully analyzed (such as (multidimensional) affine processes, sticky Lévy processes orDoeblin´s mostly unknown proposal for diffusion processes)as well as some open problems they suggest.
17:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43