Jeffrey Ezra Hoffstein | |
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| Born | November 28, 1953 New York City |
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Jeffrey Ezra Hoffstein (born September 28,1953 in New York City) [1] is an American mathematician,specializing in number theory,automorphic forms,and cryptography. [2]
Hoffstein graduated with a bachelor's degree in 1974 from Cornell University. He received his Ph.D. in 1978 from Massachusetts Institute of Technology with thesis Class numbers of totally complex quadratic extensions of totally real fields under the supervision of Harold Stark. [3] Hoffstein was a postdoc at the Institute for Advanced Study and then at the University of Cambridge. From 1980 to 1982 he was an assistant professor at Brown University. From 1982 he was an assistant professor and then an associate professor at the University of Rochester. Since 1989 he is a full professor at Brown University and he was the chair of the mathematics department from 2009 to 2013 and again from 2019 to 2024. [4]
His research uses analytic and algebraic methods to investigate L-series of automorphic forms over GL(n) and number fields. With co-workers he has developed new techniques for Dirichlet series in several complex variables. He was several times a visiting scholar at the Institute for Advanced Study (1978/79,1985,1986/87). [5] At MSRI,in the academic year 1994/95 he initiated seminars on automorphic functions. In 1984 he was a Fulbright Fellow. He was a visiting professor at the University of Texas at Austin in the spring of 1984 and at the University of Göttingen in the fall of 1986. [4] He became a Fellow of the American Mathematical Society in the class of 2019.
In 1996,Hoffstein,along with Jill Pipher,Joseph Silverman,and Daniel Liemann (Hoffstein's former doctoral student),founded NTRU Cryptosystems,Inc. to market their cryptographic algorithms,NTRUEncrypt and NTRUSign. NTRU Cryptosystems was acquired by Security Innovation in 2009. [6]
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.
NTRU is an open-source public-key cryptosystem that uses lattice-based cryptography to encrypt and decrypt data. It consists of two algorithms: NTRUEncrypt, which is used for encryption, and NTRUSign, which is used for digital signatures. Unlike other popular public-key cryptosystems, it is resistant to attacks using Shor's algorithm. NTRUEncrypt was patented, but it was placed in the public domain in 2017. NTRUSign is patented, but it can be used by software under the GPL.
Joseph Hillel Silverman is a professor of mathematics at Brown University working in arithmetic geometry, arithmetic dynamics, and cryptography.
In number theory, Tate's thesis is the 1950 PhD thesis of John Tate completed under the supervision of Emil Artin at Princeton University. In it, Tate used a translation invariant integration on the locally compact group of ideles to lift the zeta function twisted by a Hecke character, i.e. a Hecke L-function, of a number field to a zeta integral and study its properties. Using harmonic analysis, more precisely the Poisson summation formula, he proved the functional equation and meromorphic continuation of the zeta integral and the Hecke L-function. He also located the poles of the twisted zeta function. His work can be viewed as an elegant and powerful reformulation of a work of Erich Hecke on the proof of the functional equation of the Hecke L-function. Erich Hecke used a generalized theta series associated to an algebraic number field and a lattice in its ring of integers.
NTRUSign, also known as the NTRU Signature Algorithm, is an NTRU public-key cryptography digital signature algorithm based on the GGH signature scheme. The original version of NTRUSign was Polynomial Authentication and Signature Scheme (PASS), and was published at CrypTEC'99. The improved version of PASS was named as NTRUSign, and was presented at the rump session of Asiacrypt 2001 and published in peer-reviewed form at the RSA Conference 2003. The 2003 publication included parameter recommendations for 80-bit security. A subsequent 2005 publication revised the parameter recommendations for 80-bit security, presented parameters that gave claimed security levels of 112, 128, 160, 192 and 256 bits, and described an algorithm to derive parameter sets at any desired security level. NTRU Cryptosystems, Inc. have applied for a patent on the algorithm.
Dorian Morris Goldfeld is an American mathematician working in analytic number theory and automorphic forms at Columbia University.
Lattice-based cryptography is the generic term for constructions of cryptographic primitives that involve lattices, either in the construction itself or in the security proof. Lattice-based constructions support important standards of post-quantum cryptography. Unlike more widely used and known public-key schemes such as the RSA, Diffie-Hellman or elliptic-curve cryptosystems — which could, theoretically, be defeated using Shor's algorithm on a quantum computer — some lattice-based constructions appear to be resistant to attack by both classical and quantum computers. Furthermore, many lattice-based constructions are considered to be secure under the assumption that certain well-studied computational lattice problems cannot be solved efficiently.
Tomio Kubota was a Japanese mathematician working in number theory. His contributions include works on p-adic L functions and real-analytic automorphic forms.
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.
Freydoon Shahidi is an Iranian American mathematician who is a Distinguished Professor of Mathematics at Purdue University in the U.S. He is known for a method of automorphic L-functions which is now known as the Langlands–Shahidi method.
Jill Catherine Pipher was the president of the American Mathematical Society. She began a two-year term in 2019. She is also the past president of the Association for Women in Mathematics, and she was the first director of the Institute for Computational and Experimental Research in Mathematics, an NSF-funded mathematics institute based in Providence, Rhode Island.
Stephen Samuel Gelbart is an American-Israeli mathematician who holds the Nicki and J. Ira Harris Professorial Chair in mathematics at the Weizmann Institute of Science in Israel. He was named a fellow of the American Mathematical Society in 2013 "for contributions to the development and dissemination of the Langlands program."
Daniel Willis Bump is a mathematician who is a professor at Stanford University. He is a fellow of the American Mathematical Society since 2015, for "contributions to number theory, representation theory, combinatorics, and random matrix theory, as well as mathematical exposition".
Stephen James Rallis was an American mathematician who worked on group representations, automorphic forms, the Siegel–Weil formula, and Langlands L-functions.
In mathematics, the Hecke algebra is the algebra generated by Hecke operators, which are named after Erich Hecke.
David Soudry is a professor of mathematics at Tel Aviv University working in number theory and automorphic forms.
Dihua Jiang is a Chinese-born American mathematician. He is a professor of mathematics at the University of Minnesota working in number theory, automorphic forms, and the Langlands program.
Adrian Ioviță is a Romanian-Canadian mathematician, specializing in arithmetic algebraic geometry and p-adic cohomology theories.
James Wesley Cogdell is an American mathematician.
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