Pablo Shmerkin
Short Intro
I am a Professor at the University of British Columbia (on leave from T. Di Tella University). My pronouns are he/him.
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
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 .
Pablo Shmerkin and Hong Wang. Dimensions of Furstenberg sets and an extension of Bourgain's projection theorem. To appear in Anal. PDE. Arxiv .
Tuomas Orponen, Pablo Shmerkin and Hong Wang. Kaufman and Falconer estimates for radial projections and a continuum version of Beck's Theorem. To appear in Geom. Funct. Anal. Arxiv.