Quantum chaos, microlocal analysis, dynamical systems, scattering theory
Semyon Dyatlov is an Associate Professor of Mathematics, effective July 2018. In July 2019 he received tenure. He joined the mathematics faculty as Assistant Professor in January 2015. Semyon obtained his Ph.D. from UC Berkeley in 2013, under the guidance of Maciej Zworski. He received a Clay Research Fellowship (2013-2018), a Sloan Research Fellowship (2017-2021), an NSF CAREER grant (2018-), the Early Career Award of the International Association of Mathematical Physics (2018), and will be an invited speaker at the ICM 2022. He also received the 2020 MIT Teaching with Digital Technology Award. In 2022, he was selected for the inaugural Mikhail Gordin Prize: awarded by the AMS and European Mathematical Society, for an early career mathematician working in probability or dynamical systems (connected to an Eastern European country). in 2022 he gave an Invited Address (PDEs section) at the International Congress of Mathematicians (ICM).
The unifying theme in Semyon's recent research is the use of microlocal analysis, which is a mathematical theory underlying the classical/quantum, or particle/wave, correspondence in physics, in combination with hyperbolic dynamics, which is a mathematical theory of strongly chaotic systems. He has worked on: (1) quantum chaos, applying the fractal uncertainty principle to lower bounds on mass of eigenfunctions and to spectral gaps for scattering resonances; (2) Pollicott-Ruelle resonances of hyperbolic dynamical systems, and relating the singularities of dynamical zeta functions to topological invariants; (3) the study of forced waves in water tanks; (4) less recently, in quasi-normal modes and resonance expansions in general relativity.