Mathematics Winter School 

14/03/2024, 18:45 — 19:00 — Room P3.10, Mathematics Building Online
Ricardo Schiappa, Instituto Superior Técnico

Resurgence, random matrices, and strings

Some of the deepest mysteries in modern Fundamental Physics pertain to the nature of gravity in the quantum regime — most notably, how to describe quantum black holes and a quantum universe. As in previous revolutions (recall the role of Riemannian Geometry in the formulation of General Relativity, or the role of Hilbert Spaces and Operator Algebras in the formulations of Quantum Mechanics and Field Theory) new Mathematics may be required to tackle these challenges. One possibility to move forward is via the use of Resurgence and Random Matrices, mathematical tools that allow us to describe the average quantum behavior of chaotic, many-body, astrophysical and cosmological systems, far beyond small perturbations — and into the heart of their full fledged nonlinear behaviors. Exact mathematical solutions to many such problems may be obtained via the use of String Theory, in this way providing a first mathematical glimpse into a tentative new revolution in our physical understanding of the Universe.

A Master Thesis in these topics will first review the general state-of-the-art, and then focus on one of the many subtopics in these fields according to the student preferences.

See also

18H45_RS.pdf