University of Alberta

Parkinson’s disease is a debilitating condition causing highly disruptive motor complications. Although this condition has long been recognized and treated medically, many aspects of the disease and its treatment are not well understood. In fact...

We propose, analyze and test Anderson-accelerated Picard iterations for solving the incompressible Navier-Stokes equations (NSE). Anderson acceleration has recently gained interest as a strategy to accelerate linear and nonlinear iterations, based on...

Ordinal outcomes are common in scientific research and everyday practice, and we often rely on regression models to make inference. A long-standing problem with such regression analyses is the lack of effective diagnostic tools for validating model...

The regularity problem for the Navier-Stokes equation is one of the biggest open problems in nonlinear PDE. In this talk, I will use the evolution equations for the strain and vorticity to derive an identity for enstrophy growth that depends only on...

We revisit the wall-crossing behaviour of solutions of a class of thermodynamic Bethe Ansatz type integral equations, expressed as sums of ''instanton corrections''. We explain how a set of tropical curves (with signs) emerges naturally from each...

Recent advances in condensed matter physics have ushered in a new era of cross-fertilization between mathematics and physics. The study of topological materials, a radically new class of quantum materials discovered in the mid-2000s and the subject...

Recently, the optimal transport distance, or so-called Wasserstein distance has been introduced to full waveform inversion to compute the misfit between two seismograms. This measure has great potential to account for time and space shifts of events...

Among modern numerical methods to solve the optimal transport problem, dynamical optimal transport (a.k.a. fluid dynamic formulation or Benamou-Brenier formulation) is one of the oldest: it consists in rewriting the problem in terms of convex...

The second-order centered (leapfrog) time-stepping scheme is commonly used in numerical models of weather and climate. The unstable computational mode is damped by applying a Robert–Asselin filter, which introduces first-order numerical errors...

Fourier’s law, or the law of heat conduction, is well-known for nearly two centuries, which states that the energy flux is proportional to the temperature gradient. However, the rigorous derivation of Fourier’s law from microscopic Hamiltonian...