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
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)