The outcome of the visit was essentially twofold. First, a series of lectures on dynamic optimal transport, its time discretisation, its entropic regularisation, and its numerical solution, with applications to fluid mechanics and mean-field games — all of which I was happy to discuss with colleagues and students. Second, together with my host Prof. Colin Cotter, his student Jacob Francis, and my PhD student Hugo Malamut, we developed and studied a numerical method based on Entropic Optimal Transport for solving the semi-geostrophic shallow water equations. This work resulted in the paper Entropic approximations of the semi-geostrophic shallow water equations (arxiv.org/abs/2507.16415), currently under review (acknowledgment is included). This setup is a prototype for the compressible semi-geostrophic which may be a next target for this approach.
It was a great pleasure to visit Professor Colin Cotter and to work at ³Ô¹ÏºÚÁÏ. This stay built naturally on a previous collaboration focused on the incompressible semi-geostrophic equations, and it was gratifying to see that partnership deepen and evolve in new directions. The visit provided a stimulating environment for both research and exchange. The stay also proved highly beneficial for my PhD student Hugo Malamut, who was exposed to a new research environment, engaged with an international group of mathematicians, and made significant contributions to the joint work. For a doctoral student, such an experience — combining immersion in cutting-edge research with the opportunity to build lasting academic connections — is invaluable.
I hope this collaboration will continue, and I look forward to future joint projects with Professor Cotter and his group.