University of Alberta

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...

In this talk I will firstly review standard Multimarginal Optimal Transport ( a fixed number N of marginals is fixed) focusing, in particular, on the applications in Quantum Mechanics (in this case the marginals are all the same and represent the...

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...

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...

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...

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...

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...

Curvature is one of the fundamental ingredients in differential geometry. People are increasingly interested in whether it is possible to think of combinatorial graphs as manifolds and a number of different notions of curvature have been proposed. I...

We consider the problem of learning an unknown function f from given data about f. The learning problem is to give an approximation fˆ to f that predicts the values of f away from the data. There are numerous settings for this learning problem...

About 100 years ago, William Henry Young and Felix Hausdorff provedthat, for a periodic L_p-integrable function, the sequence of its Fourier coefficients necessarily lies in the discrete \ell_{p'} space provided that p' is the conjugate of p and 1