I mainly focus on calculus of variations, and more precisely on optimal transport theory and the geometry of the Wasserstein space. The specific problems that I address include:
- Incompressible Euler equations à la Brenier;
- Variational Mean Field Games;
- Harmonic mappings valued in the Wasserstein space.
List of publications
- Lavenant Hugo. Harmonic mappings valued in the Wasserstein space. 2017. Submitted paper.
- Lavenant Hugo and Santambrogio Filippo. Optimal density evolution with congestion: L infinity bounds via flow interchange techniques and applications to variational Mean Field Games. 2017. Accepted paper: Communications in PDEs.
- Lavenant Hugo. Time-convexity of the entropy in the multiphasic formulation of the incompressible Euler equation. 2017. Accepted paper: Calculus of Variations and PDEs.
- Lavenant Hugo, Naletov Vladimir, Klein Olivier, De Loubens Grégoire, Casado Laura, and De Teresa José Maria. Mechanical magnetometry of Cobalt nanospheres deposited by focused electron beam at the tip of ultra-soft cantilevers. 2014. Nanofabrication, 1(1).
You can find below works that I did before starting my PhD.
- My master thesis in history of science (September 2016, in French). It was realized under the supervision of Laurent Mazliak and was about the history of the teaching of probability calculus and statistics in France.
- My master thesis in mathematics (September 2015, in French). It was realized under the supervision of Filippo Santambrogio.
- My internship report of Master 1 (November 2014). It summarizes the work done during an intership at CalTech (United States of America) under the supervision of Oscar Bruno and Edwin Jimenez about stability problems in numerical analysis.