Department of Mathematical and Computational Sciences

University of Toronto Mississauga

3359 Mississauga Road

Deerfield Hall, Room 3017

Mississauga, ON L5L 1C6

** Email: ** tobias.hurth@utoronto.ca

I am a postdoctoral fellow in mathematics at the University of Toronto Mississauga (UTM). My supervisor is Konstantin Khanin .

I received my PhD from Georgia Tech , under the supervision of Yuri Bakhtin .

This fall, I am teaching MAT244 (Differential Equations). In recent semesters, I taught the following courses:

- Fall 2015/ Winter 2016: MAT137 Calculus
- Winter 2015: MAT236 Vector Calculus
- Fall 2014: MAT233 Calculus of Several Variables

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, Sean Lawley , Jonathan Mattingly and I are currently studying invariant densities for particular PDMPs in two dimensions.

* 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.