Luca Lionni

Researcher at CNRS


Laboratoire de Physique, ENS de Lyon
46, allée d'Italie,
69007 Lyon, France.
luca.lionni (at)ens-lyon.fr

 

 

Research:

My research is at the intersection of several areas of mathematics and physics. On the mathematical side, my specialties are random matrices and random tensors, free probability theory, and the topological, geometrical and combinatorial properties of permutation systems and discrete spaces in arbitrary dimensions (combinatorial maps, constellations, cellular complexes, colored triangulations, etc). While some of my work is purely mathematical, many of the problems I work on find their motivations and applications in theoretical physics, in quantum information and quantum gravity mainly.

In quantum physics, my work mostly concerns multipartite entanglement, randomized measurements, and the properties of random quantum states. It mathematically involves studying certain properties of matrices and tensors, random or not. Local unitary invariance of functions and distributions of matrix and tensor variables plays a central role in this context. The moments characterizing invariant random tensors induce distributions on discrete geometries of arbitrary dimensions. In quantum gravity, the mathematical description of space-time at a quantum level motivates the search for universality classes of scale-invariant random geometries. Furthermore, random tensor networks provide toy-models to study the holographic relation between entanglement and geometry.

List of preprints and articles below.

Curriculum:

I defended my PhD in September 2017, on random tensor models and the topology, geometry and combinatorics of colored triangulations (link to the manuscript in the publication list below). My PhD advisors were Valentin Bonzom and Vincent Rivasseau. I was then a postdoc in Bangkok, Kyoto, Paris, Nijmegen and Heidelberg. Since February 2024, I am a tenured researcher in Lyon (chargé de recherche).

Organization:

Grants, etc:

2025: Principal investigator of the ANR JCJC grant "RTFPQuEnt" (Random Tensors, Free Probability, and Quantum Entanglement) — 2025: member of the ANR PRC grant "TAGADA" (High dimensional random tensors and applications) — 2025: member of CNRS IRP project "QG-QS-QB" — 2024: CNRS Tremplin grant — 2018: JSPS research grant — 2018: Springer thesis prize.

Students:

2024 to 2027: Johann Chevrier, M2 internship (ENS Saclay) and then PhD, co-advised with Sylvain Carrozza
2023/24: Mathieu Dabrowski, M2 internship (ENS Lyon), co-advised with Sylvain Carrozza
2022/23: Miao Hu, M2 internship (Heidelberg University), co-advised with Razvan Gurau.

Publications:

All on arXiv. See also Google Scholar.