Under construction.

Stochastic Navier-Stokes equations (Prof. Sylvie Monniaux, A/Prof. Pierre Portal)

We aim to develop a global in time well-posedness theory for 3D Stochastic Navier-Stokes equations with critically rough data. To do so, we use stochastic maximal regularity in tent spaces, regularisation by noise, and critical spaces theory.

Categorification and geometric group theory (Dr Hoel Queffelec, Prof. Anthony Licata, Dr Asilata Bapat, Dr Anand Deopurkar)

Just like mapping class groups acting on surfaces are better studied by looking at their action on curves of the surface, we explore geometric consequences of the action of Artin-Tits groups on Khovanov-Seidel's categories and their spherical objects. The moduli space of stability conditions plays a central role, and allows for example to study faithfulness questions of the Burau representation.

See our papers on geometric consequences, Thurston compactification, and faithfulness questions.

Magnetic Dirac operators (Prof. Vincent Bruneau, Dr Galina Levitina)

This project focuses on quantifying the accumulation of eigenvalues and resonances of the perturbed magnetic Dirac operator near Landau levels, using techniques from scattering theory to analyze their distribution and dependence on the magnetic field strength.