John Torrence Tate Jr. was an American mathematician distinguished for many fundamental contributions in algebraic number theory, arithmetic geometry, and related areas in algebraic geometry. He was awarded the Abel Prize in 2010.
Don Bernard Zagier is an American-German mathematician whose main area of work is number theory. He is currently one of the directors of the Max Planck Institute for Mathematics in Bonn, Germany. He was a professor at the Collège de France in Paris from 2006 to 2014. Since October 2014, he is also a Distinguished Staff Associate at the International Centre for Theoretical Physics (ICTP).
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.
In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties.
In number theory and algebraic geometry, the Tate conjecture is a 1963 conjecture of John Tate that would describe the algebraic cycles on a variety in terms of a more computable invariant, the Galois representation on étale cohomology. The conjecture is a central problem in the theory of algebraic cycles. It can be considered an arithmetic analog of the Hodge conjecture.
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.
David Eisenbud is an American mathematician. He is a professor of mathematics at the University of California, Berkeley and former director of the then Mathematical Sciences Research Institute (MSRI), now known as Simons Laufer Mathematical Sciences Institute (SLMath). He served as Director of MSRI from 1997 to 2007, and then again from 2013 to 2022.
Lucien Serge Szpiro was a French mathematician known for his work in number theory, arithmetic geometry, and commutative algebra. He formulated Szpiro's conjecture and was a Distinguished Professor at the CUNY Graduate Center and an emeritus Director of Research at the CNRS.
Sujatha Ramdorai is an algebraic number theorist known for her work on Iwasawa theory. She is a professor of mathematics and Canada Research Chair at University of British Columbia, Canada. She was previously a professor at Tata Institute of Fundamental Research.
Annamalai Ramanathan was an Indian mathematician in the field of algebraic geometry, who introduced the notion of Frobenius splitting of algebraic varieties jointly with Vikram Bhagvandas Mehta in. The notion of Frobenius splitting led to the solution of many classical problems, in particular a proof of the Demazure character formula and results on the equations defining Schubert varieties in general flag manifolds.
Vikram Bhagvandas Mehta was an Indian mathematician who worked on algebraic geometry and vector bundles. Together with Annamalai Ramanathan he introduced the notion of Frobenius split varieties, which led to the solution of several problems about Schubert varieties. He is also known to have worked, from the 2000s onward, on the fundamental group scheme. It was precisely in the year 2002 when he and Subramanian published a proof of a conjecture by Madhav V. Nori that brought back into the limelight the theory of an object that until then had met with little success.
Richard Paul Winsley Thomas is a British mathematician working in several areas of geometry. He is a professor at Imperial College London. He studies moduli problems in algebraic geometry, and ‘mirror symmetry’—a phenomenon in pure mathematics predicted by string theory in theoretical physics.
In algebraic geometry and number theory, the torsion conjecture or uniform boundedness conjecture for torsion points for abelian varieties states that the order of the torsion group of an abelian variety over a number field can be bounded in terms of the dimension of the variety and the number field. A stronger version of the conjecture is that the torsion is bounded in terms of the dimension of the variety and the degree of the number field. The torsion conjecture has been completely resolved in the case of elliptic curves.
Indranil Biswas is an Indian mathematician. He is professor of mathematics at the Tata Institute of Fundamental Research, Mumbai. He is known for his work in the areas of algebraic geometry, differential geometry, and deformation quantization.
David Archibald Cox is a retired American mathematician, working in algebraic geometry.
Karen Ellen Smith is an American mathematician, specializing in commutative algebra and algebraic geometry. She completed her bachelor's degree in mathematics at Princeton University before earning her PhD in mathematics at the University of Michigan in 1993. Currently she is the Keeler Professor of Mathematics at the University of Michigan. In addition to being a researcher in algebraic geometry and commutative algebra, Smith with others wrote the textbook An Invitation to Algebraic Geometry.
Neena Gupta is a professor at the Statistics and Mathematics Unit of the Indian Statistical Institute (ISI), Kolkata. Her primary fields of interest are commutative algebra and affine algebraic geometry.
Jun-Muk Hwang is a South Korean mathematician, specializing in algebraic geometry and complex differential geometry.
In mathematics, a Siegel modular variety or Siegel moduli space is an algebraic variety that parametrizes certain types of abelian varieties of a fixed dimension. More precisely, Siegel modular varieties are the moduli spaces of principally polarized abelian varieties of a fixed dimension. They are named after Carl Ludwig Siegel, the 20th-century German number theorist who introduced the varieties in 1943.
Bhargav Bhatt is a mathematician who is the Fernholz Joint Professor at the Institute for Advanced Study and Princeton University and works in arithmetic geometry and commutative algebra.
