2024 OIST Workshop

Geometric Aspects of Partial Differential Equations

January 15 - 18, 2024

Nowadays an increasingly close connection has been developed between partial differential equations and geometry. The past years have witnessed applications of PDEs to a wide variety of geometry related problems arising in both pure mathematics and applied sciences such as isoperimetric problems, surface evolution, control theory, image processing, and optimal transport. On the other hand, geometric analysis also provides many novel techniques to help us understand fundamental properties of PDEs including convex structure, spectral information and asymptotic behavior. 

The purpose of this workshop is to present recent progress and new trends in PDEs from geometric perspectives. It aims to bring together the world’s leading experts and provide an international forum for researchers who are interested in this field. We plan to discuss various topics on PDEs with emphasis on geometric aspects including convexity of solutions, shape analysis, asymptotic behavior, eigenvalue problems, overdetermined problems, geometric functional inequalities, etc. With an interdisciplinary scope, this workshop also pays attention to numerous applications of recent PDE results to other related areas.

Venue: B250 (Center Building) or Zoom

Zoom Registration: Click here to get a Zoom link for online participation.

Monday, Jan. 15

10:00-11:00 Rolando Magnanini (University of Florence)

New integral identities for torsional creep functions and applications

 

11:30-12:30 Megumi Sano (Hiroshima University)

Weighted Trudinger-Moser inequalities in the subcritical Sobolev spaces and their applications

 

14:00-15:00 Ben Weinkove (Northwestern University)

Evolution equations and convexity

 

15:30-16:30 Norihisa Ikoma (Keio University)

The mountain pass theorem for nonsmooth functionals and its application

 

17:00-18:00 Katie Gittins (Durham University)

The heat content of polygonal domains

 

Tuesday, Jan. 16

10:00-11:00 Pengfei Guan (McGill University)

Constrained mean curvature flow and isoperimetric problem

 

11:30-12:30 Shinya Okabe (Tohoku University)

Dynamical approach to a generalized isoperimetric inequality

 

14:00-15:00 Cristina Trombetti (University of Napels Federico II)

Some isoperimetric estimates for Robin eigenvalues

 

15:30-16:30 Ryuichi Sato (Fukuoka University)

Existence of global-in-time solutions to a system of fully nonlinear parabolic equations

 

17:00-18:00 Karoly Boroczky (Alfred Renyi Institute of Mathematics)

Uniqueness when the \(L_p\) curvature is close to be a constant for \(p\in[0,1)\)

 

Wednesday, Jan. 17

10:00-11:00 Shigeru Sakaguchi (Tohoku University)

Symmetry in overdetermined obstacle problems

 

11:30-12:30 Xinan Ma (University of Science and Techonology of China)

Jerison-Lee identity semi-linear subelliptic equation on CR manifold

 

14:00-15:00 Hiroshi Iriyeh (Ibaraki University)

A sharp estimate of the volume product of convex bodies by means of equipartition

 

15:30-16:30 Carlo Nitsch (University of Napels Federico II)

On the gradient rearrangement of a function: the BV case

 

17:00-18:00 Alessio Figalli (ETH Zurich)

Generic regularity in obstacle problems

 

Thursday, Jan. 18

9:30-10:30 Daniel Hauer (University of Sydney)

An extension problem for the logarithmic Laplacian

 

10:45-11:45 Xiaodan Zhou (OIST)

Discontinuous eikonal equations in metric measure spaces

 

 

Talk Abstracts: A program booklet including the abstracts of all talks is available here.

 

Organizers: Kazuhiro Ishige (University of Tokyo), Qing Liu (OIST), Paolo Salani (University of Florence)

 

Code of conduct