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.

On a nonlinear kinetic Fokker-Planck equation : Cauchy problem and diffusion asymptotics  Version PDF

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.

Witten Deformation on Non-compact Manifolds  Version PDF