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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.
In number theory, the Heegner theorem establishes the complete list of the quadratic imaginary number fields whose rings of integers are principal ideal domains. It solves a special case of Gauss's class number problem of determining the number of imaginary quadratic fields that have a given fixed class number.
In mathematics, the Birch and Swinnerton-Dyer conjecture describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory and is widely recognized as one of the most challenging mathematical problems. It is named after mathematicians Bryan John Birch and Peter Swinnerton-Dyer, who developed the conjecture during the first half of the 1960s with the help of machine computation. Only special cases of the conjecture have been proven.
In mathematics, the Gauss class number problem, as usually understood, is to provide for each n ≥ 1 a complete list of imaginary quadratic fields having class number n. It is named after Carl Friedrich Gauss. It can also be stated in terms of discriminants. There are related questions for real quadratic fields and for the behavior as .
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Bryan John Birch FRS is a British mathematician. His name has been given to the Birch and Swinnerton-Dyer conjecture.
In number theory, the Stark conjectures, introduced by Stark and later expanded by Tate, give conjectural information about the coefficient of the leading term in the Taylor expansion of an Artin L-function associated with a Galois extension K/k of algebraic number fields. The conjectures generalize the analytic class number formula expressing the leading coefficient of the Taylor series for the Dedekind zeta function of a number field as the product of a regulator related to S-units of the field and a rational number.
In mathematics, a Heegner point is a point on a modular curve that is the image of a quadratic imaginary point of the upper half-plane. They were defined by Bryan Birch and named after Kurt Heegner, who used similar ideas to prove Gauss's conjecture on imaginary quadratic fields of class number one.
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In mathematics, the Gan–Gross–Prasad conjecture is a restriction problem in the representation theory of real or p-adic Lie groups posed by Gan Wee Teck, Benedict Gross, and Dipendra Prasad. The problem originated from a conjecture of Gross and Prasad for special orthogonal groups but was later generalized to include all four classical groups. In the cases considered, it is known that the multiplicity of the restrictions is at most one and the conjecture describes when the multiplicity is precisely one.
Gan Wee Teck is a Malaysian-born Singaporean mathematician. He is a Distinguished Professor of Mathematics at the National University of Singapore (NUS). He is known for his work on automorphic forms and representation theory in the context of the Langlands program, especially the theory of theta correspondence, the Gan–Gross–Prasad conjecture and the Langlands program for Brylinski–Deligne covering groups.
Samit Dasgupta is a professor of mathematics at Duke University working in algebraic number theory.
References
- ↑ Eisner <deisner@ucsd.edu>, Daryl. "UCSD Math | Profile for Benedict Gross". UCSD Math | Profile for Benedict Gross.
- 1 2 3 Curriculum vitae from Gross' web site at Harvard, retrieved 2010-04-21.
- ↑ Kirby, Rob. "Benedict H. Gross: Becoming a mathematician", Celebratio Mathematica, 2023. Accessed December 4, 2024. "Dick was born in South Orange, New Jersey on June 22, 1950, the day his sister Ruth graduated from high school and his brother Av graduated from junior high.... Even so, by his tenth grade year, Dick had exhausted the offerings at West Orange High School so he transferred to the Pingry School, a private school about ten miles from home."
- ↑ Benedict Gross at the Mathematics Genealogy Project
- ↑ Gross Officially Named Dean of the College, Harvard Crimson , April 8, 2003; Gross Stretches to Prepare for New Roles, Harvard Crimson , May 16, 2003; With Goals Accomplished, Gross Leaves Overhauled College: His efforts were to 'improve the undergraduate experience,' dean says, Harvard Crimson , June 29, 2007; Exit Gross, Harvard Crimson , September 21, 2007.
- ↑ "It's My Turn (1980) Snake Lemma". YouTube . 12 January 2009. Archived from the original on 2021-12-22.
- ↑ "Benedict Gross – Miscellaneous Crew". IMDb.com.
- ↑ "Lights, Camera and Algebraic Topology". thecrimson.com. 2003-10-23. Retrieved 2023-12-31.
- ↑ "Benedict H. Gross". MacArthur Foundation. 2023-12-14. Retrieved 2023-12-31.
- ↑ Frank Nelson Cole Prize in Number Theory, AMS, retrieved 2010-04-21.
- ↑ List of Fellows of the American Mathematical Society, retrieved 2013-01-19.
- ↑ List of Active Members by Classes Archived 2005-05-06 at the Wayback Machine , American Academy of Arts and Sciences, retrieved 2010-04-21.
- ↑ National Academies news: 72 new members chosen by academy Archived 2016-03-03 at the Wayback Machine , The National Academies, April 2004, retrieved 2010-04-21.
- ↑ "American Philosophical Society: Newly Elected – April 2017". Archived from the original on 2017-09-15. Retrieved 2017-06-13.
