Academic Report of School of Mathematical Sciences [2026] No. 062

(Series Report for High-Level University Construction No. 1321)

Title：Conformal Geometry: From the Yamabe Problem to the AdS/CFT Duality

Speaker：Wei Yuan,  Professor (Sun Yat-sen University)

Time：14:30-15:30, June 23, 2026

Location：Room 1420, Huiwen Building, Yuehai Campus

Abstract: Conformal geometry emerged at the same time that the great mathematician Gauss founded differential geometry. It has extensive and profound connections with many disciplines, including complex analysis, partial differential equations, and modern physics, and is an ancient yet vibrant field of research. This talk will briefly introduce the development of modern conformal geometry along two main threads: one begins with the famous Millennium Problem—the Poincaré Conjecture—to introduce the well-known Yamabe problem in conformal geometry; the other explores Einstein’s ultimate dream—the theory of everything—to provide a brief overview of the research framework in contemporary conformal geometry and the AdS-CFT duality theory in modern physics. It is hoped that this report will enhance the understanding and interest of students and young scholars in the field of conformal geometry.

Speaker Profile：Dr. Wei Yuan is a professor in the School of Mathematics at Sun Yat-sen University. He received his bachelor’s degree from Nankai University in 2008 and his master’s degree in science from the University of Science and Technology of China in 2010. He then pursued his studies at the University of California, Santa Cruz (UC Santa Cruz), where he earned his Ph.D. in science in 2015. His primary research interests are geometric analysis and general relativity. He has previously conducted academic visits to the Institut Poincaré (IHP) at the University of Paris VI in France, the Schrödinger Institute (ESI) at the University of Vienna in Austria, and the Korea Institute for Advanced Study (KIAS) in South Korea. To date, he has published over ten research papers in academic journals such as Math. Ann., Trans. Amer. Math. Soc., Adv. Math, Anal. PDE, and Calc. Var. Partial Differential Equations. His research primarily includes studies on Brown-York-type mass, volume comparison theorems for volume and curvature, and eigenvalue estimates, as well as research on static vacuum spacetimes with Professor Qingjie from the University of California, Santa Cruz; and research on Q-curvature, general Riemannian invariant deformations, and geometric analysis on conformally compact Einsteinian manifolds.

Faculty and students are welcome to attend!

Invited by: Ze Zhou

School of Mathematical Sciences

June 16, 2026