## 13 janvier 2021

Yuzhe Zhu (ENS)
On a nonlinear kinetic Fokker-Planck equation : Cauchy problem and diffusion asymptotics

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Lieu : https://bbb.imo.universite-paris-saclay.fr/b/nic-jog-f24-z6j

Résumé : We will discuss the concepts of hypoellipticity, hypocoercivity and relative entropy to study the Cauchy problem and the diffusion asymptotics for nonlinear kinetic drift-diffusion models. We begin with the global well-posedness under the non-perturbative regime by means of mass-spreading and regularizing results. Then, we consider its scaling limit to see the connection between the overdamped dynamics of the nonlinear kinetic model and the correlated anomalous diffusion.

Xianzhe Dai (Santa Barbara)
Witten Deformation on Non-compact Manifolds

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Lieu : Demander le lien Zoom à jean-michel.bismut@universite-paris-saclay.fr

Résumé : Witten deformation is a deformation of the de Rham complex introduced in an extremely influential paper by Witten. Witten deformation on closed manifolds has found many beautiful applications, among them the work of Bismut-Zhang on the Cheeger-M\"uller Theorem/Ray-Singer Conjecture. Development in mirror symmetry, in particular the Calabi-Yau/Landau-Ginzburg correspondence has highlighted the importance of mathematical study of Landau-Ginzburg models. This leads to a whole range of questions on the Witten deformation on non-compact manifolds. In this talk we will discuss our recent work, joint with Junrong Yan, on the $L^2$-cohomology, the heat asymptotic expansion, the local index theorem, and the Ray-Singer analytic torsion in this setting.

janvier 2021 :
 Département de Mathématiques Bâtiment 307 Faculté des Sciences d'Orsay Université Paris-Saclay F-91405 Orsay Cedex Tél. : +33 (0) 1-69-15-79-56 Département Fermeture du département Laboratoire Formation