Speaker: Prof. Xujia Wang(Westlake University)
Time: 2025-04-01 16:30-17:30
Venue: Lecture Hall 644
Abstract：The Monge-Ampere equation has significant applications in fields such as optimal transport, optical imaging, convex geometry, differential and affine geometry, and has been extensively studied in recent years, substantial new advances have been achieved in both theory and applications. In this lecture, we will introduce various applications of the Monge-Ampere equation and their extensions, and discuss new breakthroughs in the study of the regularity theory. The Monge-Ampere equation is a class of fully nonlinear partial differential equation with strong singularity, it exhibits strong inherent characteristics that makes conventional numerical methods unsatisfactory. We will also present a fast and stable computational approach to its numerical solutions.
Professor Wang Xujia primarily conducts research on the theory of nonlinear elliptic and parabolic equations and their applications, achieving a series of profound results. He resolved S.S. Chern's affine Bernstein problem conjecture and Monge's original optimal transport problem. His groundbreaking work includes contributions to the regularity and potential theory of Monge-Ampère-type equations and the characterization of singularities in mean curvature flow.
In 2002, he was awarded the Australian Mathematical Society Medal. In 2007, he received the Morningside Gold Medal of Mathematics at the Fourth International Congress of Chinese Mathematicians. He was elected as a Fellow of the Australian Academy of Science in 2009. In 2013, he was granted an Australian Laureate Fellowship.
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