Défense publique de thèse de doctorat en Sciences mathématiques - Riccardo MUOLO
Symmetry breaking and Turing patterns on networks and higher-order structures. NONLINEAR BEASTS AND WHERE TO FIND THEM
Date : 20/04/2023 17:00 - 20/04/2023 20:00
Lieu : Auditorium Rosalind Franklin (S01)
Orateur(s) : Riccardo MUOLO
Organisateur(s) : Timoteo Carletti
Jury
- Prof. Anne-Sophie LIBERT (département de mathématiques, UNamur), présidente
- Prof. Timoteo CARLETTI (département de mathématiques, UNamur), secrétaire
- Prof. Ginestra BIANCONI (Queen Mary College, London, UK)
- Prof. Francesca DI PATTI (Università degli studi di Perugia, Italie)
- Prof. Mattia FRASCA (Università degli studi di Catania, Italie)
- Prof. Hiroya NAKAO (Tokyo Institute of Technology, Japon)
Abstract
In the 50s, Alan Turing introduced and described a pattern-formation
mechanism involving two interacting chemical species driven by
diffusion. Since then, Turing patterns have been found in chemical,
biological and even quantum systems, just to mention a few. In 2010, the
theory was then extended to networked systems by Nakao and Mikhailov,
opening a new framework with great potential.
In
this thesis we study the emergence of Turing patterns on networks and
their generalizations; moreover, we establish a bridge with the theory
of synchronization by emphasizing the similarities existing between the
two frameworks. We then show how the network formalism is versatile and
well-suited to study the emergence of new forms of Turing-like patterns,
which would not be possible to obtain in its original framework, and
how to better understand their phenomenological characterization. In the
second part of the work, we further extend the theory to the new and
exciting framework of many-body and high-order interactions. Instead of a
network, the support is given by high-order structures such as
hypergraphs and simplicial complexes. Stressing again the analogy
between the synchronization framework and the Turing one, we develop a
theory of Turing patterns on hypergraphs by extending an elegant and
powerful formalism developed from synchronization. Finally, by using the
mathematical tools of algebraic topology, we study diffusion-driven
instabilities for topological signals defined on simplicial complexes.
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