I am currently a PhD. student at the Département de Mathématiques et Applications (DMA) at École Normale Supérieure in Paris under the supervision of Pierre Pansu and Claude Viterbo.

You can contact me at daniel DOT perez AT ens.fr. My office is C15, Espace Cartan at the DMA, École Normale Supérieure, 45 rue d'Ulm, 75005 Paris.

I defended my thesis on the 11th of July 2022, you can find the slides of the presentation here, as well as the online retransmission of the latter here. The manuscript of my thesis is also accessible here.

My PhD. is about persistence theory (more precisely, persistent homology) and its applications to Riemannian geometry and probability theory. Roughly speaking, the idea is to assign a family of vector spaces to a filtrated topological space in order to be able to describe this filtration and its terminal object's topology. These families of vector spaces can be assigned in such a way that they describe the topology of the superlevel or sublevel sets of the filtration.

You can read an quick and easy introduction to my line of research here.

During the Fall 2019 semester, I taught the exercise sessions for the courses "Algèbre pour physiciens" (M259) and "Mathématiques de la modélisation" (M191) at Université Paris-Saclay. In 2020, I taught M259, as well as "Intégration" (MDD302) in the fall and "Algèbre linéaire 2" (M252) in the winter at Université Paris-Saclay.

A more detailed CV is available here et une copie en français est aussi disponible ici.