Department of Mathematical and Computational Sciences
University of Toronto Mississauga
3359 Mississauga Road
Deerfield Hall, Room 3017
Mississauga, ON L5L 1C6
I am a postdoctoral fellow in mathematics at the University of Toronto Mississauga (UTM). My supervisor is Konstantin Khanin .
This fall, I am teaching MAT244 (Differential Equations). In recent semesters, I taught the following courses:
My research interests lie in probability, dynamical systems and ergodic theory.
In particular, I have been working on dynamical systems with random switching,
also known as piecewise deterministic Markov processes (PDMP),
and on directed polymers in a random environment.
In the paper below, we show how hypoellipticity of the governing vector fields of a PDMP leads to uniqueness
and absolute continuity of the invariant measure.
Yuri Bakhtin, Tobias Hurth, Invariant densities for dynamical systems with random switching http://arxiv.org/abs/1203.5744 - Nonlinearity 25 (2012) 2937-2952.
In this paper, we analyze the asymptotic behavior of the invariant densities near critical points of the vector fields in one dimension.
Yuri Bakhtin, Tobias Hurth, Jonathan C. Mattingly, Regularity of invariant densities for 1D-systems with random switching http://arxiv.org/abs/1406.5425 - Nonlinearity 28 (2015) 3755-3787.
Yuri Bakhtin, Tobias Hurth, Sean Lawley, Jonathan Mattingly, Smoothness of invariant densities for systems with random switching on the torus. In preparation.
Yuri Bakhtin, Tobias Hurth, Sean Lawley, Jonathan Mattingly, Invariant densities for a system of two randomly switched linear ODEs in two dimensions. In preparation.
Konstantin Khanin, Beatriz Navarro Lameda and I have shown a central limit theorem for a semidiscrete directed polymer-model in space dimension 3 or higher
and are currently working on deriving from this a one force - one solution principle for the semidiscrete stochastic heat equation.