Pablo Shmerkin
I am a Professor at the University of British Columbia (on leave from T. Di Tella University and Conicet). My pronouns are he/him.
My work generally spans the areas of fractal geometry, ergodic theory and analysis, although I am also interested in connections to probability and combinatorics.
In particular, my recent work is concerned with:
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Geometric properties of (random and deterministic) fractals of dynamical, arithmetic and combinatorial origin. In particular, geometrical aspects of dynamical rigidity and smoothness of self-similar measures.
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Combinatorial problems in fractal geometry (distance sets, direction sets, Kakeya-type sets, projection theorems, etc).
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Applications of fractal geometry in ergodic theory and analysis.
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Self-affine sets and the subadditive thermodynamic formalism.
RECENT ARTICLES
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Pablo Shmerkin and Ville Suomala. New bounds on Cantor maximal operators. https://arxiv.org/abs/2106.14818 .
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Tuomas Orponen and Pablo Shmerkin. On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane. https://arxiv.org/abs/2106.03338 .
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Pablo Shmerkin. A nonlinear version of Bourgain's projection theorem. https://arxiv.org/abs/2003.01636 .
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Pablo Shmerkin. On the packing dimension of Furstenberg sets. J. Anal. Math., accepted for publication. https://arxiv.org/abs/2006.15569 .
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Aleksi Pyörälä, Pablo Shmerkin, Ville Suomala and Meng Wu. Covering the Sierpinski carpet with tubes. https://arxiv.org/abs/2006.00499.
UPCOMING EVENTS
Interactions between Geometric measure theory, Singular integrals, and PDE