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

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 .
Amir Algom and Pablo Shmerkin. On the dimension of orthogonal projections of self-similar measures. Arxiv
Tuomas Orponen, Nicolas de Saxcé and Pablo Shmerkin. On the Fourier decay of multiplicative convolutions. Arxiv .
Tuomas Orponen and Pablo Shmerkin. Projections, Furstenberg sets, and the ABC sum-product problem. Arxiv .

Recent and upcoming conferences and event organization

SLMath hot topics workshop: Interactions between Harmonic Analysis, Homogeneous Dynamics and Number Theory, 3-7 March, 2025.
Workshop on Dynamical Systems and related topics, University of Maryland, USA, 3-5 April 2025.
12th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial, Spain, 9-13 June, 2025
3rd joint meeting UMA-RSME (Mathematical societies of Argentina and Spain), December 1-5, 2025 .
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.