Biography

I did my undergraduate degree (Licenciatura) at the University of Buenos Aires. My Licenciatura thesis was supervised by Ursula Molter .

I then moved to Seattle to complete a PhD at the University of Washington with Boris Solomyak. 

Afterwards, I was a postdoc at the University of Jyväskylä (working with Esa and Maarit Järvenpää), a research member at MSRI during the program in ergodic theory and additive combinatorics, and a postdoc at the University of Manchester, within the CICADA group. I came to Surrey in May 2011 as a Leverhulme Early Career Fellow.

I've given short courses at the University of Buenos Aires, Argentina (2010), University of Oulu, Finland (2011) and University of Mar del Plata, Argentina (2011), and had research stays at IMPA, Microsoft Research, Chinese University of Hong Kong, and University of Helsinki, among others.

Research Interests

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

In particular, my recent work is concerned with:

• Geometric properties of (random and deterministic) fractals of dynamical and combinatorial origin.
• Applications of fractal geometry in ergodic theory and analysis. 
• New connections between geometric measure theory and ergodic theory.

Publications

Submitted:

• T. Sahlsten, P. Shmerkin and V. Suomala. Dimension, entropy, and the local distribution of measures . http://arxiv.org/abs/1110.6011

Accepted:

• M. Hochman and P. Shmerkin. Local entropy averages and projections of fractal measures. To appear in Annals of Math. http://arxiv.org/abs/0910.1956.
• P.. Shmerkin. The dimension of weakly mean porous measures: a probabilistic approach. To appear in International Mathematical Research Notices. http://arxiv.org/abs/1010.1394.
• F. Nazarov, Y. Peres and P. Shmerkin. Convolutions of Cantor measures without resonance. To appear in Israel Journal of Math. http://arxiv.org/abs/0905.3850.
• T. Jordan, P. Shmerkin and B. Solomyak. Multifractal structure of Bernoulli convolutions. To appear in Math. Proceedings of the Cambridge Philosophical Society. http://arxiv.org/abs/1011.1938
• I. Arhosalo, E. Järvenpää, M. Jäärvenpää, M. Rams and P. Shmerkin. Visible parts of fractal percolation. To appear in Proceedings of the Edinburgh Mathematical Society. http://arxiv.org/abs/0911.3931

Appeared:

• P. Shmerkin. Porosity, dimension, and local entropies: a survey. Revista de la Unión Matemática Argentina 52 (2011), no 2, 81-103.
• J. Schmeling and P. Shmerkin. On the dimension of iterated sumsets. Recent developments in fractals and related fields, 55–72. Birkhäuser Boston, Inc., Boston, MA, 2010. http://arxiv.org/abs/0906.1537
• A. Ferguson, T. Jordan and P. Shmerkin. The Hausdorff dimension of the projections of self-affine carpets. Fund. Math 209 (2010), no 3, 193-213. http://arxiv.org/abs/0903.2216
• A. Käenmäki and P. Shmerkin. Overlapping self-affine sets of Kakeya type. Ergodic Theory Dynam. Systems 29 (2009), no 3, 941-965. http://arxiv.org/abs/0710.0442.
• Y. Peres and P. Shmerkin. Resonance between Cantor sets. Ergodic Theory Dynam. Systems 29 (2009), no 1, 201-221.http://arxiv.org/abs/0705.2628.
• P. Shmerkin and B. Solomyak. Zeros of  {-1,0,1} power series and connectedness loci for self-affine sets . Experiment. Math. 15 (2006), no 4, 499-511. http://arxiv.org/abs/math/0504545.
• P. Shmerkin. Overlapping self-affine sets. Indiana Univ. Math. J. 55 (2006), no. 4, 1291-1331. http://arxiv.org/abs/math/0408203.
• P. Shmerkin. A modified multifractal formalism for a class of self-similar measures. Asian J. Math. 9 (2005), no. 3, 323-348. http://arxiv.org/abs/math/0408047.

E-mail

My e-mail is (initial of first name)(dot)(last name)(at)surrey(dot)ac(dot)uk