Pablo Shmerkin

Short Intro

I am a Professor at the University of British Columbia. My pronouns are he/him. I'm part of the Harmonic Analysis and Fractal Geometry group at UBC.

My work generally spans the areas of fractal geometry, analysis, and ergodic theory, although I am also interested in connections between these fields and probability and combinatorics.

In particular, my recent work is concerned with:

Combinatorial problems in fractal geometry (projection theory, distance sets, Furstenberg set problem, etc).
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.
Applications of fractal geometry in ergodic theory and analysis.

Recent articles

Alan Chang, Pablo Shmerkin and Ville Suomala. Sharp Favard length of random Cantor sets. Arxiv.
William O'Regan, Pablo Shmerkin and Hong Wang. Simple proofs of discretized projection theorems. Arxiv.
Pablo Shmerkin and Alexia Yavicoli. Full measure universality for Cantor sets. Arxiv .
Pablo Shmerkin and Ville Suomala. The largest slice of fractal percolation. Arxiv .
Emilio Corso and Pablo Shmerkin. Dynamical self-similarity, $L^q$ dimensions and Furstenberg slicing in $\mathbb{R}^d$. Arxiv .
Tuomas Orponen, Nicolas de Saxcé and Pablo Shmerkin. On the Fourier decay of multiplicative convolutions. Arxiv .

Upcoming conferences and event organization

Semester "Interactions between Fractal Geometry, Harmonic Analysis and Dynamical Systems", Institut Mittag-Leffler, Stockholm, Sweden, September 2-December 11, 2026. Co-organizer, with Michael Björklund, Tuomas Orponen, Tuomas Sahlsten and Hong Wang. Note: The program is by invitation only, has a very limited number of spots and is currently oversubscribed.
Fractals and Related Fields 5, Porquerolles, France, June 8-12, 2026.
Dynamics, Equations, and Applications, Krakow, Poland, June 28-July 2, 2027.