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Number Theory And Physics: October 24-November 18 2022

Organized by:
Brian Conrey (American Institute of Mathematics ),
Matilde Lalin (Université de Montréal),
Giuseppe Mussardo (Laboratorio Interdisciplinare Scienze Naturali e Umanistiche, SISSA),
German Sierra (UAM/CSIC)

The interplay between Number Theory and Physics has a long tradition, as illustrated by several examples and many initiatives of the past. A well-know example is the tantalizing connection between Random Matrix Theory and the statistical properties of the zeros of the Riemann zeta function and other L-functions. This connection opened the avenue to the application of techniques that first appeared in Nuclear Physics to Number Theory. Random Matrix Theory has proved to be a golden mine of profound ideas which span from the description of random media to cold atom fermions in magnetic trap. It is worth to mention that it is along this direction the attempt to address the Riemann Hypothesis employing concepts from Quantum Mechanics or Statistical Physics. String theory has also provided a playground for the connections with number theory and algebraic geometry, playing an important role in the discovery of mirror symmetry. Many novel ideas are now emerging relating string theory and the geometry of Calabi-Yau manifolds to Mock modular forms and paramodular forms. Finally, Number Theory has also played a crucial role in Quantum Information starting from the Shor’s algorithm that reduces the exponential cost of factorizing integers in a classical computer to a polynomial cost using a quantum computer. The recent construction of small quantum computers suggests that quantum algorithms based on Number Theory will play a fundamental role in the near future with a huge impact in basic sciences and technology.

There is also a workshop associated with this event: Number Theory And Physics.