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 Hong Wang. On the distance sets spanned by sets of dimension d/2 in R^d. https://arxiv.org/abs/2112.09044 .

Amir Algom, Simon Baker and Pablo Shmerkin. On normal numbers and selfsimilar measures. https://arxiv.org/abs/2111.10082 . To appear in Advances in Math.

Pablo Shmerkin. Slices and distances: on two problems of Furstenberg and Falconer. https://arxiv.org/abs/2109.12157 . This is my contribution to the ICM 2022 Proceedings and provides a high level overview of recent progress around Furstenberg's slicing conjecture and the Falconer distance set problem.

Pablo Shmerkin and Ville Suomala. New bounds on Cantor maximal operators. https://arxiv.org/abs/2106.14818 . To appear in the special issue of Rev. Un. Mat. Argentina dedicated to the Mathematical Congress of the Americas 2021.

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.To appear in J. Eur. Math. Soc. (JEMS). https://arxiv.org/abs/2003.01636 .
UPCOMING EVENTS
Interactions between Geometric measure theory, Singular integrals, and PDE