Education

MSc Mathematics

Moscow Phystech

PhD Mathematics,

Caltech

Publications

Full list of publications

Research Interests

My research profile embraces problems that lie at the intersection of harmonic analysis, geometric and additive combinatorics, with some links to number theory. These problems can be often interpreted within the framework of geometric incidence theory and theorems of Szemerédi-Trotter type, which ask for combinatorial bounds on the size of the intersection of two families of geometric objects, one of which may be, for instance, a finite point set, and the other -- a set of curves or surfaces. A notable example of questions of this type are the distance conjectures of Erdös and Falconer. They are related to other major open questions, such as the Erdös ring problem and Kakeya. Additionally, I retain some interest in my mother-field, which is Hamiltonian dynamics; more precisely those are issues of integrability and onsets for non-integrability.

Research Themes

• Combinatorics
• Geometric Group Theory