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:

Geometric properties of (random and deterministic) fractals of dynamical, arithmetic and combinatorial origin. In particular, geometrical aspects of dynamical rigidity and smoothness of selfsimilar measures.

Combinatorial problems in fractal geometry (distance sets, direction sets, Kakeyatype sets, projection theorems, etc).

Applications of fractal geometry in ergodic theory and analysis.

Selfaffine sets and the subadditive thermodynamic formalism.
RECENT ARTICLES

Pablo Shmerkin and Ville Suomala. New bounds on Cantor maximal operators. https://arxiv.org/abs/2106.14818 .

Tuomas Orponen and Pablo Shmerkin. On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane. https://arxiv.org/abs/2106.03338 .

Pablo Shmerkin. A nonlinear version of Bourgain's projection theorem. https://arxiv.org/abs/2003.01636 .

Pablo Shmerkin. On the packing dimension of Furstenberg sets. J. Anal. Math., accepted for publication. https://arxiv.org/abs/2006.15569 .

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