# Contact&Bio

## Contact Information

Department of Mathematics, University of Brisith Columbia

Office 210, 1984 Mathematics Road, Vancouver, BC, V6T 1Z2, Canada

E-mail: pshmerkin@math.ubc.ca

Note: I try to reply to all serious e-mail (examples of non-serious e-mails are invitations to publish in predatory journals or outlandish claims about proofs of famous problems). However, I am busy so it can take a while. I may also overlook some e-mails, so feel free to send a polite reminder.

## About me

I was an enthusiastic participant in math olympics in Argentina during high school. I did my undergraduate degree at the Department of Mathematics of the University of Buenos Aires. I then moved to the University of Washington to complete my PhD under the supervision of Boris Solomyak.

Afterwards I held postdoc positions at the universities of Jyväskylä (Finland) and Manchester (UK) and was a research fellow at the University of Surrey (UK). I was also a member of MSRI for a semester in 2008, of ICERM in 2016 and of Mittag-Leffler institute in 2017.

In 2003 I returned to Argentina to join the Department of Mathematics and Statistics of Torcuato Di Tella University as an associate professor. I was also an independent researcher at CONICET from 2014 to 2020.

I joined UBC's Math Department in 2020.

I've given short courses at the University of Buenos Aires, Argentina (2010 and 2015), University of Oulu, Finland (2011), University of Mar del Plata, Argentina (2011), University of Jyväskylä, Finland (2015), CIRM, France (2019), and had research stays at IMPA, Microsoft Research, Chinese University of Hong Kong, University of Helsinki, Hebrew University of Jerusalem, the University of St Andrews and Cambridge University.

In July 2016 I received the UMALCA prize at the Vth Latin American Congress of Mathematicians in Barranquilla, Colombia. In July 2017 I was awaded the MCA prize at the Mathematical Congress of the Americas in Montréal, Canada. In August 2018 I received the Bunge&Born Stimulus Prize, awarded in Mathematics for the first time. I delivered an invited talk at the Analysis section of the 2022 International Congress of Mathematicians.

I serve on the editorial boards of Revista de la Unión Matemática Argentina, Journal of Fractal Geometry, Ergodic Theory and Dynamical Systems and International Mathematical Research Notices. To submit a paper to any of these journals, please follow the instructions on the websites (do not send papers directly to me).

## Research interests

Projection theory and discretized incidences. Size of projections and incidences between fractal-like discrete structures.

Geometric measure theory. Geometric properties of sets and measures in Euclidean space: porosity, conical densities, etc.

Harmonic analysis. Fourier decay of fractal measures, problems of Kakeya type, maximal operator of fractal type

Structures in fractal sets. Geometric configurations (distance sets, radial projections, arithmetic progressions) in fractals

Ergodic theory. Geometric aspects of dynamical rigidity. Sums and intersections of invariant Cantor sets. Normal numbers.

Self-similar and self-affine sets measures. Dimension, absolute continuity and geometric properties of self-similar and self-affine measures