On the Erdős-Volkmann and Katz-Tao ring conjectures

By Jean Bourgain. 2003

154 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/652da0549d6448dc106906c7db5d611cb784984a

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

Citations in the corpus

Incidence Estimates for Well Spaced Tubes (2019, background): “rectangles) in [0, 1].”
New Bounds on the Dimensions of Planar Distance Sets (2018, unknown): “Later Bourgain [2], crucially relying on earlier work of N.”
On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane (2021, result): “As mentioned already, it follows by combining results of Katz-Tao [10] and Bourgain [1] that s-Furstenberg sets have Hausdorff dimension at least 1 ` for s "very close" to 1 2 .”
Stationary measures and equidistribution for orbits of nonabelian semigroups on the torus (2011, methodology): “5] of the first author (based on techniques developed in the context of the Discretized Ring Conjecture [4]).”
The discretized sum-product and projection theorems (2010, methodology): “This result was obtained in [ B ] under a stronger non-concentration property with κ replaced with σ− in (0.1).”
On the dimension and smoothness of radial projections (2017, methodology): “8 is possible, combining the proof below with ideas from the paper [6] of Katz and Tao, and using the discretised sum-product theorem of Bourgain [2].”
Recent progress on Bernoulli convolutions (2016, methodology): “This result can be thought of as an entropy analogue of the additive part in the proof of Bourgain’s discretized sum product theorem [4], [5].”
On the spectral gap for finitely-generated subgroups of SU(2) (2007, methodology): “In fact, we need a technical strengthening of the result in [ 2 ], which is given in Proposition 3.2 proved in Sect.”