Welcome to my homepage! I am Gabriele Todeschi, postdoctoral researcher at the Institut Camille Jordan working within the ERC project EYAWKAJKOS led by Filippo Santambrogio.

My research activity revolves around optimal transport, its numerical approximation and its application to modeling purposes. I am particularly interested in variational methods, as well as in the design and analysis of numerical schemes that preserve the structure of the underlying problems. A central concern is to understand how geometric properties of the underlying spaces are lifted through optimal transport. Applications I consider include the theory of Wasserstein gradient flows, which is related to certain types of partial differential equations, the design of algorithms based on the geometry of optimal transport for optimization in the space of probability measures, the application to inverse problems. The common thread is the development of robust and efficient numerical methods grounded in convex optimization. I recently started to explore how tools from convex analysis can be extended to broader nonlinear and nonsmooth settings.

Previously, I was a postdoctoral researcher at the CERMICS Laboratory of the École Nationale des Ponts et Chaussées, where I collaborated with Virginie Ehrlacher. Our focus was the extension of metric properties of optimal transport to its quantum counterpart. Before that, I was a postdoctoral researcher in the group New challenging Monge problems and their applications of the Labex Bézout, Université Gustave Eiffel, working under the supervision of François-Xavier Vialard on the geometry of spaces of probability measures endowed with an optimal transport cost. Even before, I held a postdoctoral position at the institute ISTerre of the Université Grenoble Alpes, working with Ludovic Mètivier (ISTerre) and Jean-Marie Mirebeau (ENS Paris-Saclay) on the application of optimal transport to seismic imaging.

I did my PhD in the Inria-Ceremade team MOKAPLAN, under the supervision of Jean-David Benamou, Thomas Gallouët (Inria, Paris) and Clément Cancès (Inria, Lille). I defended my thesis in December 2021. The objective was to develop efficient and reliable numerical tools to solve the quadratic optimal transport problem and Wasserstein gradient flows. I was also a fellow of the Marie Sklodowska-Curie Cofund MathInParis Doctoral Program of the Fondation Sciences Mathématiques de Paris (FSMP).

You can find my complete cv here.