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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.
"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
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 ...
In 1999, Wolff posed the finite field analogue to the Kakeya problem, in hopes that the techniques for solving this conjecture could be carried over to the Euclidean case. 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 ...
The Mahler conjecture holds for zonotopes. [6] The Mahler conjecture holds in the class of unconditional bodies, that is, convex bodies invariant under reflection on each coordinate hyperplane {x i = 0}. This was first proven by Saint-Raymond in 1980. [7] Later, a much shorter proof was found by Meyer. [8]
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 ...
Former President Donald Trump falsely said Friday that a decades-old photo of him with E. Jean Carroll, the writer he has been found liable for sexually abusing and defaming, might have been ...
"Made contributions in differential equations, also to the Calabi conjecture in algebraic geometry, to the positive mass conjecture of general relativity theory, and to real and complex Monge–Ampère equations." [63] 1986 Berkeley, US Simon Donaldson: University of Oxford, UK Imperial College London, UK [66] Stony Brook University, US [67]