In mathematics, the Langlands program is a set of conjectures about connections between number theory and geometry. It was proposed by Robert Langlands. It seeks to relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and adeles. It is the biggest project in mathematical research. It was described by Edward Frenkel as "grand unified theory of mathematics."
Gorō Shimura was a Japanese mathematician and Michael Henry Strater Professor Emeritus of Mathematics at Princeton University who worked in number theory, automorphic forms, and arithmetic geometry. He was known for developing the theory of complex multiplication of abelian varieties and Shimura varieties, as well as posing the Taniyama–Shimura conjecture which ultimately led to the proof of Fermat's Last Theorem.
Peter David Lax is a Hungarian-born American mathematician and Abel Prize laureate working in the areas of pure and applied mathematics.
Richard Peter Stanley is an Emeritus Professor of Mathematics at the Massachusetts Institute of Technology, and an Arts and Sciences Distinguished Scholar at the University of Miami. From 2000 to 2010, he was the Norman Levinson Professor of Applied Mathematics. He received his Ph.D. at Harvard University in 1971 under the supervision of Gian-Carlo Rota. He is an expert in the field of combinatorics and its applications to other mathematical disciplines.
Joseph Hillel Silverman is a professor of mathematics at Brown University working in arithmetic geometry, arithmetic dynamics, and cryptography.
Daniel J. Kleitman is an American mathematician and professor of applied mathematics at MIT. His research interests include combinatorics, graph theory, genomics, and operations research.
Dorian Morris Goldfeld is an American mathematician working in analytic number theory and automorphic forms at Columbia University.
In mathematics, the local Langlands conjectures, introduced by Robert Langlands, are part of the Langlands program. They describe a correspondence between the complex representations of a reductive algebraic group G over a local field F, and representations of the Langlands group of F into the L-group of G. This correspondence is not a bijection in general. The conjectures can be thought of as a generalization of local class field theory from abelian Galois groups to non-abelian Galois groups.
Henryk Iwaniec is a Polish-American mathematician, and since 1987 a professor at Rutgers University. He is a member of the American Academy of Arts and Sciences and Polish Academy of Sciences. He has made important contributions to analytic and algebraic number theory as well as harmonic analysis. He is the recipient of Cole Prize (2002), Steele Prize (2011), and Shaw Prize (2015).
In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis.
Gil Kalai is an Israeli mathematician and computer scientist. He is the Henry and Manya Noskwith Professor Emeritus of Mathematics at the Hebrew University of Jerusalem, Israel, Professor of Computer Science at the Interdisciplinary Center, Herzliya, and adjunct Professor of mathematics and of computer science at Yale University, United States.
János Kollár is a Hungarian mathematician, specializing in algebraic geometry.
Percy Alec Deift is a mathematician known for his work on spectral theory, integrable systems, random matrix theory and Riemann–Hilbert problems.
In mathematics, the Rankin–Selberg method, introduced by Rankin and Selberg, also known as the theory of integral representations of L-functions, is a technique for directly constructing and analytically continuing several important examples of automorphic L-functions. Some authors reserve the term for a special type of integral representation, namely those that involve an Eisenstein series. It has been one of the most powerful techniques for studying the Langlands program.
Nolan Russell Wallach is a mathematician known for work in the representation theory of reductive algebraic groups. He is the author of the two-volume treatise Real Reductive Groups.
Alexander Nikolaevich Varchenko is a Soviet and Russian mathematician working in geometry, topology, combinatorics and mathematical physics.
James Edward Humphreys was an American mathematician who worked in algebraic groups, Lie groups, and Lie algebras and applications of these mathematical structures. He is known as the author of several mathematical texts, such as Introduction to Lie Algebras and Representation Theory and Reflection Groups and Coxeter Groups.
Haruzo Hida is a Japanese mathematician, known for his research in number theory, algebraic geometry, and modular forms.
Stephen Carl Milne is an American mathematician who works in the fields of analysis, analytic number theory, and combinatorics.
Jeffrey Ezra Hoffstein is an American mathematician, specializing in number theory, automorphic forms, and cryptography.
