Yuri Ivanovich Manin was a Russian mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics.
Shou-Wu Zhang is a Chinese-American mathematician known for his work in number theory and arithmetic geometry. He is currently a Professor of Mathematics at Princeton University.
Hiraku Nakajima is a Japanese mathematician, and a professor of the Kavli Institute for the Physics and Mathematics of the Universe at the University of Tokyo. He is International Mathematical Union president for the 2023–2026 term.
John Willard Morgan is an American mathematician known for his contributions to topology and geometry. He is a Professor Emeritus at Columbia University and a member of the Simons Center for Geometry and Physics at Stony Brook University.
In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, which is a non-singular variety W with a proper birational map W→V. For varieties over fields of characteristic 0, this was proved by Heisuke Hironaka in 1964; while for varieties of dimension at least 4 over fields of characteristic p, it is an open problem.
In mathematics, the Bogomolov conjecture is a conjecture, named after Fedor Bogomolov, in arithmetic geometry about algebraic curves that generalizes the Manin-Mumford conjecture in arithmetic geometry. The conjecture was proven by Emmanuel Ullmo and Shou-Wu Zhang in 1998 using Arakelov theory. A further generalization to general abelian varieties was also proved by Zhang in 1998.
In algebraic geometry, a variety over a field k is ruled if it is birational to the product of the projective line with some variety over k. A variety is uniruled if it is covered by a family of rational curves. The concept arose from the ruled surfaces of 19th-century geometry, meaning surfaces in affine space or projective space which are covered by lines. Uniruled varieties can be considered to be relatively simple among all varieties, although there are many of them.
Noncommutative algebraic geometry is a branch of mathematics, and more specifically a direction in noncommutative geometry, that studies the geometric properties of formal duals of non-commutative algebraic objects such as rings as well as geometric objects derived from them.
Kai Behrend is a German mathematician. He is a professor at the University of British Columbia in Vancouver, British Columbia, Canada.
William Messing is an American mathematician who works in the field of arithmetic algebraic geometry.
In commutative algebra and algebraic geometry, Popescu's theorem, introduced by Dorin Popescu, states:
The Stacks Project is an open source collaborative mathematics textbook writing project with the aim to cover "algebraic stacks and the algebraic geometry needed to define them". As of July 2022, the book consists of 115 chapters spreading over 7500 pages. The maintainer of the project, who reviews and accepts the changes, is Aise Johan de Jong.
Victor Vadimovich Batyrev is a Russian mathematician, specializing in algebraic and arithmetic geometry and its applications to mathematical physics. He is a professor at the University of Tübingen.
Carlos Tschudi Simpson is an American mathematician, specializing in algebraic geometry.
Mark Lee Green is an American mathematician, who does research in commutative algebra, algebraic geometry, Hodge theory, differential geometry, and the theory of several complex variables. He is known for Green's Conjecture on syzygies of canonical curves.
Emmanuel Ullmo is a French mathematician, specialised in arithmetic geometry. Since 2013 he has served as director of the Institut des Hautes Études scientifiques.
Frans Oort is a Dutch mathematician who specializes in algebraic geometry.
Joseph Henri Maria Steenbrink is a Dutch mathematician, specializing in algebraic geometry.
Ronald Alan Fintushel is an American mathematician, specializing in low-dimensional geometric topology and the mathematics of gauge theory.
Bhargav Bhatt is an Indian-American mathematician who is the Fernholz Joint Professor at the Institute for Advanced Study and Princeton University and works in arithmetic geometry and commutative algebra.
