A l'origine, la conférence était prévue en présentiel, dans le respect des gestes barrières.

Toutefois, depuis l'annonce du reconfinement général en France, la conférence aura lieu en dématérialisé. Le lien zoom sera envoyé sur la mailing list du GDR TRAG.

Au cas, où vous seriez intéressé d'avoir le lien, n'hésitez pas à nous écrire!

Ismael Bailleul: Structures de régularités et calcul paracontrôlé
Résumé : Je décrirai dans cet exposé certains des liens qu'on peut faire entre les concepts fondamentaux des structures de régularité et ceux du calcul paracontrôlé, ainsi que les bénéfices qu'on peut en tirer.

Florian Bechtold: A Law of Large Numbers for interacting diffusions via a mild formulation
Résumé: Consider a system of $n$ weakly interacting particles driven by independent Brownian motions. In many instances, it is well known that the empirical measure converges to the solution of a partial differential equation, usually called McKean-Vlasov or Fokker-Planck equation, as $n$ tends to infinity. We propose a relatively new approach to show this convergence by directly studying the stochastic partial differential equation that the empirical measure satisfies for each fixed $n$. Under a suitable control on the noise term, which appears due to the finiteness of the system, we are able to prove that the stochastic perturbation goes to zero, showing that the limiting measure is a solution to the classical McKean-Vlasov equation. In contrast with known results, we do not require any independence or finite moment assumption on the initial condition, but the only weak convergence. The evolution of the empirical measure is studied in a suitable class of Hilbert spaces where the noise term is controlled using two distinct but complementary techniques: rough paths theory and maximal inequalities for self-normalized processes.

Youness Boutaib: Path classification with continuous-time recurrent neural networks
Résumé: We seek mathematical learning guarantees for path-classification tasks using stochastic (linear, in this talk) recurrent networks with continuous-time rate dynamics. This architecture finds its origin in neuroscience and is simple as training only requires finding a pre-processing projection vector and the parameters of a read-out map. We give generalisation error bounds and argue that stochasticity provides learning with a robustness against adversarial attacks. We also explicitly show that training (in the case of our loss function) is equivalent to an optimisation problem of a functional on the signatures of the training paths. This is an ongoing joint work with S. Nestler (FZ Jülich) and H. Rauhut (RWTH Aachen).

Rémi Catellier: Regularization by noise for rough differential equations.
Résumé : After an overview on regularization by noise for stochastic differential equations, and in particular for the multiplicative case, we introduce a controlled path structure à la Gubinelli to deal with this problem in the rough path setting. We give an application to the fractional Brownian motion case. This talk is base on a ongoing work with Romain Duboscq.

Łukasz Mądry: Reflected differential equations