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Jean Louis, baron Bourgain (French:; () 28 February 1954 – () 22 December 2018) was a Belgian mathematician. He was awarded the Fields Medal in 1994 in recognition of his work on several core topics of mathematical analysis such as the geometry of Banach spaces, harmonic analysis, ergodic theory and nonlinear partial differential equations from mathematical physics.
As reformulated, it became the "paving conjecture" for Euclidean spaces, and then a question on random polynomials, in which latter form it was solved affirmatively. 2015: Jean Bourgain, Ciprian Demeter, and Larry Guth: Main conjecture in Vinogradov's mean-value theorem: analytic number theory: Bourgain–Demeter–Guth theorem, ⇐ decoupling ...
Finite Field Kakeya Conjecture: Let F be a finite field, let K ⊆ F n be a Kakeya set, i.e. for each vector y ∈ F n there exists x ∈ F n such that K contains a line {x + ty : t ∈ F}. Then the set K has size at least c n |F| n where c n >0 is a constant that only depends on n. Zeev Dvir proved this conjecture in 2008, showing that the ...
"for spectacular contributions to low dimensional topology and geometric group theory, including work on the solutions of the tameness, virtually Haken and virtual fibering conjectures." [10] [11] University of California, Berkeley Institute for Advanced Study: 2017: Jean Bourgain (1954–2018) Belgium
Theorem (Bourgain, Katz, Tao (2004)): [23] Let p be prime and let A ⊂ 픽 p with p δ < | A | < p 1−δ for some 0 < δ < 1. Then max(| A + A |, | AA |) ≥ c δ | A | 1+ε for some ε = ε(δ) > 0. Bourgain, Katz, and Tao extended this theorem to arbitrary fields. Informally, the following theorem says that if a sufficiently large set does ...
Bourgain [17] 13/84 0.1548 Bourgain ... Bourgain, Jean ... "A conjecture for the sixth power moment of the Riemann zeta-function", International Mathematics Research ...
2018 Jean Bourgain; 2017 James G. Arthur; 2016 Barry Simon; 2015 Victor Kac; ... This is the paper that introduced what are now known as the Langlands conjectures. 2004
Vinogradov's proof was a byproduct of the odd Goldbach conjecture, that every sufficiently large odd number is the sum of three primes. George Birkhoff , in 1931, and Aleksandr Khinchin , in 1933, proved that the generalization x + na , for almost all x , is equidistributed on any Lebesgue measurable subset of the unit interval.