Polina Perstneva is currently studying to receive a Ph.D. from Université Paris-Saclay, under the directed of Prof. Guy David. She received her B.S. in Mathematics from Saint-Petersburg State University in 2019 and has worked on several undergrad and graduate theses:
Master thesis: “Harmonic measure in high co-dimensions” under supervision of Professor Guy David (grade 18, general diploma note Bien),
Bachelor thesis: “Theorems of de Leeuw-Katznelson-Kahane type on the two-dimensional torus” under the supervision of professor Sergey Kislyakov (diploma with distinction).
Harmonic analysis (Fourier coefficients behaviour in functional classes: theorems of De Leeuw - Katznelson - Kahane type and connected statements, operators - multipliers, Men‘shov-type correction theorems, uncertainty principals)
Geometric analysis (harmonic measure in Rn, counterexamples to its absolute continuity to the surface measure, harmonic measure for sets of high co-dimensions, analogues to Dahlberg’s theorem for the latter setting)
Dynamical systems, mathematical physics (hysteresis, operators spectrum and properties)
Minor interests include:
Bellman function, TCS (classical algorithms, Machine Learning, AI and Godel‘s incompleteness theorem), combinatorics and geometry (geodesics and Laplace operator spectrum on surfaces).
Honors and Awards
Winner of MIPT math olympiad (2014), prize winner of OMMO (2014)
Prize winner of Saint-Petersburg stage of All-Russian physics and astronomy olympiads (2014)
Special diploma of Sakharov‘s Reading for poster, physics section, 2014
Scholarship of “Gazprom Neft” prize winner (2016 - 2019)
Fondation Math ́ematique Jaсques Hadamard scholarshiper (2019 - 2020)
Kislyakov S.V., Perstneva P.S. “Indicator functions with uniformly bounded Fourier sums and large gaps in the spectrum”, arxiv.org/abs/2006.02561, 2020,
Aleksandr Enin, Polina Perstneva, Sergey Tikhomirov. “Periodic solutions of parabolic equations with hysteresis in dimension 1”, Zap. Nauchn. Sem. POMI, Volume 489, pp 36-54, 2020 (to be translated in Journal of Mathematical Sciences).