Pablo Shmerkin
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. Arxiv .
-
Tuomas Orponen, Pablo Shmerkin and Hong Wang. Kaufman and Falconer estimates for radial projections and a continuum version of Beck's Theorem. Arxiv.