Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric. This gives, in particular, local notions of angle, length of curves, surface area and volume. From those, some other global quantities can be derived by integrating local contributions.
Grigori Yakovlevich Perelman is a Russian mathematician who is known for his contributions to the fields of geometric analysis, Riemannian geometry, and geometric topology. In 2005, Perelman abruptly quit his research job at the Steklov Institute of Mathematics, and in 2006 stated that he had quit professional mathematics, due to feeling disappointed over the ethical standards in the field. He lives in seclusion in Saint Petersburg, and has not accepted offers for interviews since 2006.
Shing-Tung Yau is a Chinese-American mathematician. He is the director of the Yau Mathematical Sciences Center at Tsinghua University and Professor Emeritus at Harvard University. Until 2022 he was the William Caspar Graustein Professor of Mathematics at Harvard, at which point he moved to Tsinghua.
Eugenio Calabi was an Italian-born American mathematician and the Thomas A. Scott Professor of Mathematics at the University of Pennsylvania, specializing in differential geometry, partial differential equations and their applications.
In the mathematical field of differential geometry, Ricci-flatness is a condition on the curvature of a Riemannian manifold. Ricci-flat manifolds are a special kind of Einstein manifold. In theoretical physics, Ricci-flat Lorentzian manifolds are of fundamental interest, as they are the solutions of Einstein's field equations in a vacuum with vanishing cosmological constant.
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.
Mikhael Leonidovich Gromov is a Russian-French mathematician known for his work in geometry, analysis and group theory. He is a permanent member of Institut des Hautes Études Scientifiques in France and a professor of mathematics at New York University.
In the mathematical field of differential geometry, there are various splitting theorems on when a pseudo-Riemannian manifold can be given as a metric product. The best-known is the Cheeger–Gromoll splitting theorem for Riemannian manifolds, although there has also been research into splitting of Lorentzian manifolds.
In mathematics, the soul theorem is a theorem of Riemannian geometry that largely reduces the study of complete manifolds of non-negative sectional curvature to that of the compact case. Jeff Cheeger and Detlef Gromoll proved the theorem in 1972 by generalizing a 1969 result of Gromoll and Wolfgang Meyer. The related soul conjecture, formulated by Cheeger and Gromoll at that time, was proved twenty years later by Grigori Perelman.
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.
The Oswald Veblen Prize in Geometry is an award granted by the American Mathematical Society for notable research in geometry or topology. It was funded in 1961 in memory of Oswald Veblen and first issued in 1964. The Veblen Prize is now worth US$5000, and is awarded every three years.
The Geometry Festival is an annual mathematics conference held in the United States.
Jean-Michel Bismut is a French mathematician who has been a professor at the Université Paris-Sud since 1981. His mathematical career covers two apparently different branches of mathematics: probability theory and differential geometry. Ideas from probability play an important role in his works on geometry.
Werner Müller is a German mathematician. His research focuses on global analysis and automorphic forms.
Tobias Holck Colding is a Danish mathematician working on geometric analysis, and low-dimensional topology. He is the great grandchild of Ludwig August Colding.
Guofang Wei is a mathematician in the field of differential geometry. She is a professor at the University of California, Santa Barbara.
Gerhard Huisken is a German mathematician whose research concerns differential geometry and partial differential equations. He is known for foundational contributions to the theory of the mean curvature flow, including Huisken's monotonicity formula, which is named after him. With Tom Ilmanen, he proved a version of the Riemannian Penrose inequality, which is a special case of the more general Penrose conjecture in general relativity.
Fernando Codá dos Santos Cavalcanti Marques is a Brazilian mathematician working mainly in geometry, topology, partial differential equations and Morse theory. He is a professor at Princeton University. In 2012, together with André Neves, he proved the Willmore conjecture. Since then, among proving other important conjectures, Marques and Neves greatly extended Almgren–Pitts min-max theory to prove theorems about minimal surfaces.
Christina Sormani is a professor of mathematics at City University of New York affiliated with Lehman College and the CUNY Graduate Center. She is known for her research in Riemannian geometry, metric geometry, and Ricci curvature, as well as her work on the notion of intrinsic flat distance.
Xiuxiong Chen is a Chinese-American mathematician whose research concerns differential geometry and differential equations. A professor at Stony Brook University since 2010, he was elected a Fellow of the American Mathematical Society in 2015 and awarded the Oswald Veblen Prize in Geometry in 2019. In 2019, he was awarded the Simons Investigator award.
