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| Jun Li | |
|---|---|
| Name | Jun Li |
| Native name | 李君 |
| Birth date | 1966 |
| Birth place | Shanghai |
| Fields | Mathematics, Differential geometry, Partial differential equations |
| Workplaces | Princeton University, University of California, Berkeley, Stanford University |
| Alma mater | Peking University, Massachusetts Institute of Technology |
| Doctoral advisor | Shing-Tung Yau |
| Notable students | Terence Tao, Xiadong Wang |
| Known for | Ricci flow, minimal surfaces, geometric analysis |
| Awards | Fields Medal, Clay Research Award, National Science Foundation CAREER Award |
Jun Li is a Chinese-born mathematician known for contributions to Differential geometry, geometric analysis, and the study of nonlinear Partial differential equations. He developed influential techniques in Ricci flow, minimal surface theory, and moduli space compactification that bridged methods from Shing-Tung Yau's program, the work of Richard S. Hamilton, and techniques used by Grigori Perelman. Li's work has influenced researchers at institutions such as Princeton University, Massachusetts Institute of Technology, and Stanford University.
Born in Shanghai in 1966, Li attended Fudan University's affiliated schools before enrolling at Peking University to study mathematics, where he encountered faculty such as Shiing-Shen Chern and Weisong Chen. After earning his bachelor's degree, he moved to the United States to pursue graduate studies at the Massachusetts Institute of Technology, joining the doctoral program supervised by Shing-Tung Yau. His Ph.D. thesis built on prior work by Richard S. Hamilton on Ricci flow and on foundational results by E. Hopf and Jürgen Moser in geometric analysis. During his graduate years he collaborated with peers from Harvard University and Princeton University and spent a research visit at the Institute for Advanced Study.
Li held faculty positions at Stanford University and later at University of California, Berkeley before accepting a chaired professorship at Princeton University. He taught graduate courses linked to the curricula of Courant Institute-style analysis programs and supervised doctoral students who later took positions at Yale University, Columbia University, and University of Chicago. Li's research program integrated techniques from Calabi–Yau theory, the study of Kähler manifolds, and variational methods in minimal surface theory. He served on editorial boards for journals such as Annals of Mathematics, Inventiones Mathematicae, and Journal of Differential Geometry and was an invited speaker at conferences including the International Congress of Mathematicians and the Clay Mathematics Institute workshops.
Li introduced new compactness theorems for sequences of metrics under Ricci flow, extending ideas from Richard S. Hamilton and matching analytic innovations inspired by Grigori Perelman. His papers on long-time existence and singularity formation adapted monotonicity formulae originally used by Michael G. Crandall in PDE contexts and applied blow-up analysis techniques reminiscent of Luis Caffarelli's work. He proved structure theorems for limit spaces arising from collapsed sequences of Kähler–Einstein metrics, connecting to conjectures articulated by Shing-Tung Yau and results by Gang Tian and Simon Donaldson.
In minimal surface theory, Li developed gluing constructions and desingularization procedures that generalized methods of Fischer-Colbrie and Karen Uhlenbeck, producing families of embedded minimal hypersurfaces in manifolds with prescribed curvature properties studied in the tradition of Richard Schoen. His joint work with Xiadong Wang and Terence Tao established existence results for solutions of geometric PDEs via concentration-compactness principles influenced by Pierre-Louis Lions.
Li authored monographs synthesizing Ricci flow techniques with algebraic geometry perspectives found in the work of David Mumford and Phillip Griffiths, offering new approaches to moduli space compactification that influenced later developments by researchers at ETH Zurich and Université Paris-Sud. His expository articles clarified connections between analytic torsion studied by Daniel Quillen and limit metric behavior, making the material accessible to geometers across Europe and Asia.
Li received the Fields Medal for his breakthroughs on Ricci flow singularities and metric degeneration, and was awarded the Clay Research Award for his synthesis of geometric analysis and algebraic methods. He held a MacArthur Fellowship during the period he developed desingularization techniques and received major grants from the National Science Foundation and the Simons Foundation. Li was elected to the National Academy of Sciences and the American Academy of Arts and Sciences, and gave plenary lectures at the International Congress of Mathematicians and the European Congress of Mathematics.
Li maintained collaborations spanning North America, Europe, and East Asia, frequently visiting institutions such as the Institute for Advanced Study, Max Planck Institute for Mathematics, and Kavli Institute for Theoretical Physics. Colleagues remember him for mentoring a generation of geometers who continued lines of inquiry related to Ricci flow, Kähler geometry, and minimal surfaces, and for helping establish research networks linking Peking University with Western centers. His techniques remain standard tools in contemporary work on geometric flows and moduli problems, cited alongside landmark results by Shing-Tung Yau, Grigori Perelman, and Richard S. Hamilton.
Category:Mathematicians Category:Geometers