119 citations · 463 across the 37 of their papers we have counts for
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Szemerédi's regularity lemma revisited
Terence Tao
Szemerédi's regularity lemma is a basic tool in graph theory, and also plays an important role in additive combinatorics, most notably in proving Szemerédi's theorem on arithmetic…
A variant of the hypergraph removal lemma
Terence Tao
Recent work of Gowers and Nagle, Rödl, Schacht, and Skokan has established a hypergraph removal lemma, which in turn implies some results of Szemerédi and Furstenberg-Katznelson co…
A quantitative ergodic theory proof of Szemerédi's theorem
Terence Tao
A famous theorem of Szemerédi asserts that given any density and any integer , any set of integers with density will contain infinitely many proper arit…
Fuglede's conjecture is false in 5 and higher dimensions
Terence Tao
We give an example of a set which is a finite union of unit cubes, such that admits an orthonormal basis of exponentials $\{\frac{1}{|Ω|^{1/2}} e^{2πi ξ_j…
A sum-product estimate in finite fields, and applications
Jean Bourgain, Nets Katz, Terence Tao
Let be a subset of a finite field for some prime . If for some , then we prove the estimate $|A+A| + |A.A| \geq c(δ) |A|^{1+\eps…
A new bound on partial sum-sets and difference-sets, and applications to the Kakeya conjecture
Nets Hawk Katz, Terence Tao
Let , be finite subsets of an abelian group, and let be such that $# A, # B, # \{a+b: (a,b) \in G \} \leq N$. We consider the question of estimating th…