Shing-Tung Yau is a Chinese-American mathematician and the William Caspar Graustein Professor of Mathematics at Harvard University. In April 2022, Yau announced retirement from Harvard to become Chair Professor of mathematics at Tsinghua University.
In differential geometry, a hyperkähler manifold is a Riemannian manifold endowed with three integrable almost complex structures that are Kähler with respect to the Riemannian metric and satisfy the quaternionic relations . In particular, it is a hypercomplex manifold. All hyperkähler manifolds are Ricci-flat and are thus Calabi–Yau manifolds.
Richard Streit Hamilton is an American mathematician who serves as the Davies Professor of Mathematics at Columbia University. He is known for contributions to geometric analysis and partial differential equations. Hamilton is best known for foundational contributions to the theory of the Ricci flow and the development of a corresponding program of techniques and ideas for resolving the Poincaré conjecture and geometrization conjecture in the field of geometric topology. Grigori Perelman built upon Hamilton's results to prove the conjectures, and was awarded a Millennium Prize for his work. However, Perelman declined the award, regarding Hamilton's contribution as being equal to his own.
Ennio De Giorgi, a member of the House of Giorgi, was an Italian mathematician who worked on partial differential equations and the foundations of mathematics.
Richard Melvin Schoen is an American mathematician known for his work in differential geometry and geometric analysis. He is best known for the resolution of the Yamabe problem in 1984.
Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and differential topology. The use of linear elliptic PDEs dates at least as far back as Hodge theory. More recently, it refers largely to the use of nonlinear partial differential equations to study geometric and topological properties of spaces, such as submanifolds of Euclidean space, Riemannian manifolds, and symplectic manifolds. This approach dates back to the work by Tibor Radó and Jesse Douglas on minimal surfaces, John Forbes Nash Jr. on isometric embeddings of Riemannian manifolds into Euclidean space, work by Louis Nirenberg on the Minkowski problem and the Weyl problem, and work by Aleksandr Danilovich Aleksandrov and Aleksei Pogorelov on convex hypersurfaces. In the 1980s fundamental contributions by Karen Uhlenbeck, Clifford Taubes, Shing-Tung Yau, Richard Schoen, and Richard Hamilton launched a particularly exciting and productive era of geometric analysis that continues to this day. A celebrated achievement was the solution to the Poincaré conjecture by Grigori Perelman, completing a program initiated and largely carried out by Richard Hamilton.
Graduate Studies in Mathematics (GSM) is a series of graduate-level textbooks in mathematics published by the American Mathematical Society (AMS). The books in this series are published in hardcover and e-book formats.
Weinan E is a Chinese mathematician. He is known for his pathbreaking work in applied mathematics and machine learning. His academic contributions include novel mathematical and computational results in stochastic differential equations; design of efficient algorithms to compute multiscale and multiphysics problems, particularly those arising in fluid dynamics and chemistry; and pioneering work on the application of deep learning techniques to scientific computing. In addition, he has worked on multiscale modeling and the study of rare events.
Maciej Zworski is a Polish, Canadian mathematician, currently a professor of mathematics at the University of California, Berkeley. His mathematical interests include microlocal analysis, scattering theory, and partial differential equations.
Alessio Figalli is an Italian mathematician working primarily on calculus of variations and partial differential equations.
Russel E. Caflisch is an American mathematician.
Irena Lasiecka is a Polish-American mathematician, a Distinguished University Professor of mathematics and chair of the mathematics department at the University of Memphis. She is also co-editor-in-chief of two academic journals, Applied Mathematics & Optimization and Evolution Equations & Control Theory.
Albert Fathi is an Egyptian-French mathematician. He specializes in dynamical systems and is currently a professor at the Georgia Institute of Technology.
Eduard Feireisl is a Czech mathematician.
Luigi Chierchia is an Italian mathematician, specializing in nonlinear differential equations, mathematical physics, and dynamical systems.
Xavier Ros Oton is a Spanish mathematician who works on partial differential equations (PDEs). He is an ICREA Research Professor and a Full Professor at the University of Barcelona.
Maria Colombo is an Italian mathematician specializing in mathematical analysis. She is a professor at the EPFL in Switzerland, where she holds the chair for mathematical analysis, calculus of variations and partial differential equations.
Grzegorz Świątek is a Polish mathematician, currently a professor at the Warsaw University of Technology. He is known for his contributions to dynamical systems.
Michael Hochman is an Israeli mathematician, currently a professor at the Hebrew University of Jerusalem. He is known for his contributions to dynamical systems and ergodic theory.
Raphaël Krikorian is a French mathematician, currently a professor at the CY Cergy Paris University. He is known for his contributions to dynamical systems.
