Research

I am primarily interested by the physics of Quantum Gravity and how this problem can be tackled using the path integral formalism by considering novel notions of discrete geometries.

My research is based on a notion of discrete spaces called combinatorial cell complexes (or simply cell complexes or cc) whose definition does not rely on any manifold or continuum structure and is equivalent to one introduced by Basak in a paper from 2010, in which he studies an analog of a Poincaré Duality. Broadly speaking, my work in particular extends this duality to cell complexes with a non-empty boundary, and this lead me to introduce a discrete notion of cobordism. When investigating how to compose cobordisms in order to form a category, I introduced a notion of causal cobordisms, which generalizes the notion of Causal Dynamical Triangulations in arbitrary finite dimension introduced by Ambjörn and Loll in 1992.

I also obtained results about how to "reconstruct" certain cell complexes dual to triangulations (i.e. simplicial complexes) using only their cells of dimension 2 and lower.

Papers

• My pre-print titled Combinatorial Cobordism Theory is on arxiv (submitted to SIGMA for reviewal ).

• I am preparing an article on the reconstruction of simple cell complexes (based on Chap. 2 of my thesis).

• Some python programming I did as an intern at Geneva Observatory was used for a paper by G. Battaglia and al. titled What is the Milky Way outer halo made of? High resolution spectroscopy of distant red giants (2017).

Thesis

• An updated version of my thesis titled Combinatorial Cell Complexes: Duality, reconstruction and causal cobordisms can be found on arxiv.

• The slides of my PhD-defense can be found here.

Talks

• My slides for the Mathematical Physics seminar at the University of Geneva, on November 15th. 2021.

• My slides for the Quantum and Gravity seminar at IMAPP (Renate Loll), on June 17th. 2022.