Tobias Hurth



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 .

Teaching:

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

Research:

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.