Lars Valerian Ahlfors was a Finnish mathematician, remembered for his work in the field of Riemann surfaces and his textbook on complex analysis.
In mathematics, the Hodge conjecture is a major unsolved problem in algebraic geometry and complex geometry that relates the algebraic topology of a non-singular complex algebraic variety to its subvarieties.
In mathematics, the uniformization theorem states that every simply connected Riemann surface is conformally equivalent to one of three Riemann surfaces: the open unit disk, the complex plane, or the Riemann sphere. The theorem is a generalization of the Riemann mapping theorem from simply connected open subsets of the plane to arbitrary simply connected Riemann surfaces.
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.
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator on a compact manifold, the analytical index is equal to the topological index. It includes many other theorems, such as the Chern–Gauss–Bonnet theorem and Riemann–Roch theorem, as special cases, and has applications to theoretical physics.
Shiing-Shen Chern was a Chinese-American mathematician and poet. He made fundamental contributions to differential geometry and topology. He has been called the "father of modern differential geometry" and is widely regarded as a leader in geometry and one of the greatest mathematicians of the twentieth century, winning numerous awards and recognition including the Wolf Prize and the inaugural Shaw Prize. In memory of Shiing-Shen Chern, the International Mathematical Union established the Chern Medal in 2010 to recognize "an individual whose accomplishments warrant the highest level of recognition for outstanding achievements in the field of mathematics".
In mathematics, the Chern theorem states that the Euler–Poincaré characteristic of a closed even-dimensional Riemannian manifold is equal to the integral of a certain polynomial of its curvature form.
Charles Louis Fefferman is an American mathematician at Princeton University, where he is currently the Herbert E. Jones, Jr. '43 University Professor of Mathematics. He was awarded the Fields Medal in 1978 for his contributions to mathematical analysis.
Jürgen Kurt Moser was a German-American mathematician, honored for work spanning over four decades, including Hamiltonian dynamical systems and partial differential equations.
In mathematics, a CR manifold, or Cauchy–Riemann manifold, is a differentiable manifold together with a geometric structure modeled on that of a real hypersurface in a complex vector space, or more generally modeled on an edge of a wedge.
In the mathematical theory of functions of one or more complex variables, and also in complex algebraic geometry, a biholomorphism or biholomorphic function is a bijective holomorphic function whose inverse is also holomorphic.
Shoshichi Kobayashi was a Japanese mathematician. He was the eldest brother of electrical engineer and computer scientist Hisashi Kobayashi. His research interests were in Riemannian and complex manifolds, transformation groups of geometric structures, and Lie algebras.
László Lempert is a Hungarian-American mathematician, working in several complex variables and complex geometry. He proved that the Carathéodory and Kobayashi distances agree on convex domains. He further proved that a compact, strictly pseudoconvex real analytic hypersurface can be embedded into the unit sphere of a Hilbert space.
Alexander Nikolaevich Varchenko is a Soviet and Russian mathematician working in geometry, topology, combinatorics and mathematical physics.
Steven Morris Zelditch was an American mathematician, specializing in global analysis, complex geometry, and mathematical physics.
Alexander Joseph Nagel is an American mathematician, specializing in harmonic analysis, functions of several complex variables, and linear partial differential equations.
Dieter Kotschick is a German mathematician, specializing in differential geometry and topology.
Serguei Barannikov is a mathematician, known for his works in algebraic topology, algebraic geometry and mathematical physics.
François Ledrappier is a French mathematician.
Tsachik Gelander is an Israeli mathematician working in the fields of Lie groups, topological groups, symmetric spaces, lattices and discrete subgroups. He is a professor in Northwestern University.
