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.
- Computational optimal transport.
List of publications
- New estimates on the regularity of the pressure in density-constrained Mean Field Games. LH and Santambrogio Filippo. 2018. Submitted paper.
- Total Variation Isoperimetric Profiles. DeFord Daryl, LH, Schutzman Zachary and Solomon Justin. 2018. Submitted paper.
- Dynamical Optimal Transport on Discrete Surfaces (supplemental, code). LH, Claici Sebastian, Chien Edward and Solomon Justin, 2018. Accepted paper: SIGGRAPH Asia 2018.
- Harmonic mappings valued in the Wasserstein space. LH. 2017. Submitted paper.
- Optimal density evolution with congestion: L infinity bounds via flow interchange techniques and applications to variational Mean Field Games. LH and Santambrogio Filippo. 2017. Accepted paper: Communications in PDEs.
- Time-convexity of the entropy in the multiphasic formulation of the incompressible Euler equation. LH. 2017. Accepted paper: Calculus of Variations and PDEs.
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.
- The research conducted during my internship at CEA Saclay (June and July 2013) under the supervision of Grégoire De Loubens led to a publication: Mechanical magnetometry of Cobalt nanospheres deposited by focused electron beam at the tip of ultra-soft cantilevers. LH, Naletov Vladimir, Klein Olivier, De Loubens Grégoire, Casado Laura, and De Teresa José Maria. 2014. Nanofabrication, 1(1).