Geordie Richards

Assistant Professor, Mathematics
Email: 
grichards@uoguelph.ca
Office: 
MacNaughton 547
Website links: 
My Research Website
Summary: 

Research Themes:

Prof. Richards’ research is focused on the analysis of deterministic and stochastic nonlinear partial differential equations (PDEs) coming from physics and engineering, specifically equations modeling fluids and dispersive (i.e., wave-like) phenomena.  Much of this work uses PDE techniques which combine nonlinear analysis with ideas from probability theory and the theory of dynamical systems.  He also conducts collaborative research with engineers and applied mathematicians on topics related to nonlinear dynamics and uncertainty quantification.

Areas of Focus:

  1. Random data for dispersive PDEs
  2. Ergodic theory of stochastic PDEs
  3. Singular stochastic PDEs
  4. Uncertainty quantification in applications

Prof. Geordie Richards received his PhD in Mathematics from the University of Toronto in 2012.  Richards previously held academic positions at the Institute for Mathematics and its Applications at the University of Minnesota (2012-2013), the Department of Mathematics at the University of Rochester (2013-2016), the Department of Mechanical & Aerospace Engineering at Utah State University (2016-2021), and the Department of Mathematical & Computational Sciences at the University of Toronto Mississauga (2021-2022).  He joined the Department of Mathematics & Statistics at the University of Guelph in 2022.

 

Areas of Focus with Select Publications:

       1. Random data for dispersive PDEs

Geordie Richards, “Invariance of the Gibbs measure for the periodic quartic gKdV”, Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 3, pp. 699–766 https://doi.org/10.1016/j.anihpc.2015.01.003.

       2. Ergodic theory of stochastic PDEs

(a) Nathan Glatt-Holtz, Vincent Martinez, Geordie Richards, “On the long-time statistical behavior of smooth solutions of the weakly damped, stochastically-driven KdV equation,” To appear in Transactions of the American Mathematical Society (2025).  Preprint available on arXiv. 

(b) Juraj Földes, Nathan Glatt-Holtz, Geordie Richards, Enrique Thomann, “Ergodic and mixing properties of the Boussinesq equations with a degenerate random forcing”, Journal of Functional Analysis 269 (2015), Issue 8, pp. 2427-2504 https://doi.org/10.1016/j.jfa.2015.05.014

       3. Singular stochastic PDEs

Geordie Richards, “Well-posedness of the stochastic KdV–Burgers equation”, Stochastic Processes and their Applications 124 (2014), Issue 4, pp. 1627-1647, https://doi.org/10.1016/j.spa.2013.12.008 

       4. Uncertainty quantification in applications

Mingyuan Nie, Jared P. Whitehead, Geordie Richards, Barton L. Smith, and Zhao Pan. "Error propagation dynamics of PIV-based pressure field calculation (3): what is the minimum resolvable pressure in a reconstructed field?." Experiments in Fluids 63 (2022), no.11,168. https://doi.org/10.1007/s00348-022-03512-8

Highlights: 

  • Nuclear Regulatory Commission (NRC) Faculty Development Grant, Utah State University, 2019-2022.
  • Mechanical & Aerospace Engineering Teacher of the Year, Utah State University, 2019.
  • Research Membership at the Simons Laufer Mathematical Sciences Institute at UC Berkeley (formerly MSRI) for thematic program on “New Challenges in PDE: Deterministic Dynamics and Randomness in High and Infinite Dimensional Systems”, September-October 2015.
  • Natural Sciences and Engineering Research Council (NSERC) Postgraduate Scholarship, 2006.