Pablo Shmerkin

Mathematical Physics · 2007–2023

A researcher in the Science corpus: 12 papers; trusts 33 researchers and is trusted by 18 researchers here, as inferred from the citation graph.

Subfields

• Mathematical Physics — 70 citations into it; #796 of 8,562 by trust here, #1,097 by citations
• Geometry and Topology — 35 citations into it; #1,868 of 7,422 by trust here, #3,077 by citations
• Applied Mathematics — 26 citations into it; #3,031 of 7,620 by trust here, #3,258 by citations
• Computational Theory and Mathematics — 14 citations into it; #2,662 of 12,182 by trust here, #5,239 by citations
• Statistical and Nonlinear Physics — 14 citations into it; #4,310 of 10,127 by trust here, #7,024 by citations
• Discrete Mathematics and Combinatorics — 13 citations into it; #775 of 2,017 by trust here, #1,251 by citations
• Computer Vision and Pattern Recognition — 5 citations into it
• Finance — 5 citations into it

Whom Pablo Shmerkin trusts overall

Their strongest outbound trust, strongest first, inferred from their citations.

1. Michael Hochman
2. Yuval Peres
3. T. Wolff
4. Jean Bourgain
5. G. Mockenhaupt
6. Boris Solomyak
7. Wilhelm Schlag
8. De-Jun Feng
9. Alexander I. Bufetov
10. Jong-Guk Bak

Who trusts Pablo Shmerkin overall

1. P. P. Varj'u
2. Meng Wu
3. Michael Hochman
4. Jonathan M. Fraser
5. Kenneth J. Falconer
6. Larry Guth
7. Tuomas Orponen
8. Ian D. Morris
9. Balázs Bárány
10. Boris Solomyak

Papers from Pablo Shmerkin's perspective

Ordered by how strongly the researchers Pablo Shmerkin trusts endorse each paper. Same corpus, a different order for every researcher.

1. Sixty Years of Bernoulli Convolutions
2. The discretized sum-product and projection theorems
3. Local entropy averages and projections of fractal measures
4. Some Connections between Falconer's Distance Set Conjecture and Sets of Furstenburg Type
5. Smoothness of projections, Bernoulli convolutions, and the dimension of exceptions
6. On natural invariant measures on generalised iterated function systems
7. Ergodic fractal measures and dimension conservation (Ergodic Theory and Dynamical Systems)
8. Nonadditive thermodynamic formalism: Equilibrium and Gibbs measures
9. Ledrappier-Young formula and exact dimensionality of self-affine measures
10. Intersections of Cantor Sets and Transversality of Semigroups

Their papers

• Local entropy averages and projections of fractal measures (2009) — 189 citations
• On Furstenberg's intersection conjecture, self-similar measures, and the Lq norms of convolutions (2016) — 183 citations
• Equidistribution from fractal measures (2013) — 78 citations
• Projections, Furstenberg sets, and the $ABC$ sum-product problem (2023) — 52 citations
• On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane (2021) — 56 citations
• New Bounds on the Dimensions of Planar Distance Sets (2018) — 48 citations
• On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems (2016) — 55 citations
• Salem sets with no arithmetic progressions (2015) — 49 citations
• Absolute continuity of self-similar measures, their projections and convolutions (2014) — 78 citations
• On the Exceptional Set for Absolute Continuity of Bernoulli Convolutions (2013) — 124 citations
• Non-conformal Repellers and the Continuity of Pressure for Matrix Cocycles (2013) — 58 citations
• Resonance between Cantor sets (2007) — 127 citations