Analysis/PDE Day Talk 1:
Nonsmooth Calculus: Gradient Estimates
Renjin Jiang, Beijing Normal University
In this talk, I will present some recent developments of nonsmooth calculus regarding gradient estimates for harmonic functions and heat kernels. Motivations from geometric analysis and PDEs as well as abstract nonsmooth calculus will be discussed, some relevant results will also be reported. We will then show the equivalence between quantitative regularity of harmonic functions and heat kernels, i.e., characterizations for Yau's gradient estimate for harmonic functions and Li-Yau's gradient estimate for heat kernels, and their natural analogies of Lp versions. Applications to the Riesz transform, Sobolev inequalities, and examples from Riemannian and sub-Riemannian geometry as well as non-smooth settings, and degenerate elliptic/parabolic equations will be discussed. Local version of the theory will also be presented.
Biography
Dr. Jiang Renjin graduated in 2012 with a degree of Doctor of Philosophy from University of Jyväskylä, Finland. He became a faculty member of School of Mathematical Sciences, Beijing Normal University, since October 2012, and a full professor since September 2016. He joined Center of Applied Mathematics, Tianjin University, by the end of 2016. From November 2014 to November 2015 he held a Marie-Curie ER position in Autonomous University of Barcelona. R. Jiang’s research interest locates in harmonic analysis, metric geometry and PDEs.
Analysis/PDE Day Talk 2:
Conically Singular Solution in Semilinear Elliptic Equations
Yong Yu, Chinese University of Hong Kong
In this talk we will firstly introduce the conically singular solution in the prescribed Gaussian curvature problem. Then I will introduce a new Born-Infeld approximation scheme to re-prove this classical result. This method will finally be generalized to a class of semilinear elliptic equations with exponential nonlinearities, in which Chern Simons-Higgs equation and gauged harmonic map equation are included. New conically singular solutions are found in these two physical models.
Biography
Yong Yu is now an assistant professor at the Chinese University of Hong Kong. He graduated from Fudan University in 2004 with a master's degree. Then he proceeded to study in NYU with Prof. Fang Hua LIN from 2004 to 2009. After graduation, he served as a visiting assistant professor at University of Iowa for 3 years.
Analysis/PDE Day Talk 3:
Global Dynamics of Competition System With Nonlocal Diffusion
Fang Li, East China Normal University
Biography
Professor Fang Li holds her PhD from University of Minnesota in 2008. She is associate professor in Center for Partial Differential Equations, East China Normal University. Her research interests are partial differential equations and applied mathematics.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai