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
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 .
Pablo Shmerkin and Alexia Yavicoli. On the volumes of simplices determined by a subset of $\mathbb{R}^d$. Arxiv.
Tuomas Orponen, Nicolas de Saxcé and Pablo Shmerkin. On the Fourier decay of multiplicative convolutions. Arxiv .
Pablo Shmerkin. Inverse theorems for discretized sums and $L^q$ norms of convolutions in $\mathbb{R}^d$. Arxiv .
Tuomas Orponen and Pablo Shmerkin. Projections, Furstenberg sets, and the ABC sum-product problem. Arxiv .
Recent and upcoming conferences and event organization
School on Dimension Theory of Fractals, Erdös Center, Budapest, Hungary, 26-30 August 2024. Minicourse "Additive Combinatorics Methods in Fractal Geometry".
Slides for minicourse: Lecture 1 | Lecture 2 | Lecture 3 | Lecture 4
CMS Winter Meeting 2024, Richmond, BC, Canada, 29 November-2 December 2024.
SLMath hot topics workshop: Interactions between Harmonic Analysis, Homogeneous Dynamics and Number Theory, 3-7 March, 2025.
12th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial, Spain, 9-13 June, 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.