Jean-Pierre Serre is a French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the inaugural Abel Prize in 2003.
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.
Pierre René, Viscount Deligne is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoord Prize, and 1978 Fields Medal.
Nicholas Michael Katz is an American mathematician, working in arithmetic geometry, particularly on p-adic methods, monodromy and moduli problems, and number theory. He is currently a professor of Mathematics at Princeton University and an editor of the journal Annals of Mathematics.
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.
Joseph Hillel Silverman is a professor of mathematics at Brown University working in arithmetic geometry, arithmetic dynamics, and cryptography.
Arnold Ephraim Ross was a mathematician and educator who founded the Ross Mathematics Program, a number theory summer program for gifted high school students. He was born in Chicago, but spent his youth in Odessa, Ukraine, where he studied with Samuil Shatunovsky. Ross returned to Chicago and enrolled in University of Chicago graduate coursework under E. H. Moore, despite his lack of formal academic training. He received his Ph.D. and married his wife, Bee, in 1931.
In arithmetic geometry, the Tate–Shafarevich groupШ(A/K) of an abelian variety A (or more generally a group scheme) defined over a number field K consists of the elements of the Weil–Châtelet group WC(A/K) = H1(GK, A) that become trivial in all of the completions of K (i.e. the p-adic fields obtained from K, as well as its real and complex completions). Thus, in terms of Galois cohomology, it can be written as
Robert Frederick Coleman was an American mathematician, and professor at the University of California, Berkeley.
Shinichi Mochizuki is a Japanese mathematician working in number theory and arithmetic geometry. He is one of the main contributors to anabelian geometry. His contributions include his solution of the Grothendieck conjecture in anabelian geometry about hyperbolic curves over number fields. Mochizuki has also worked in Hodge–Arakelov theory and p-adic Teichmüller theory. Mochizuki developed inter-universal Teichmüller theory, which has attracted attention from non-mathematicians due to claims it provides a resolution of the abc conjecture.
Ralph Greenberg is an American mathematician who has made contributions to number theory, in particular Iwasawa theory.
Michael Ira Rosen is an American mathematician who works on algebraic number theory, arithmetic theory of function fields, and arithmetic algebraic geometry.
Lawrence Clinton Washington is an American mathematician at the University of Maryland, who specializes in number theory.
Haruzo Hida is a Japanese mathematician, known for his research in number theory, algebraic geometry, and modular forms.
Vincent Pilloni is a French mathematician, specializing in arithmetic geometry and the Langlands program.
Jennifer Shyamala Sayaka Balakrishnan is an American mathematician known for leading a team that solved the problem of the "cursed curve", a Diophantine equation that was known for being "famously difficult". More generally, Balakrishnan specializes in algorithmic number theory and arithmetic geometry. She is the Clare Boothe Luce Associate Professor at Boston University.
Jack A. Thorne is a British mathematician working in number theory and arithmetic aspects of the Langlands Program. He specialises in algebraic number theory.
Christopher McLean Skinner is an American mathematician working in number theory and arithmetic aspects of the Langlands program. He specialises in algebraic number theory.
Sergei Alekseevich Evdokimov was a Russian mathematician who contributed to the theory of modular forms, computational complexity theory, algebraic combinatorics and p-adic analysis.
Adrian Ioviță is a Romanian-Canadian mathematician, specializing in arithmetic algebraic geometry and p-adic cohomology theories.
