Workshop: Number Theory And Physics: October 24 – October 28, 2022

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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 workshop is associated with the program: Number Theory And Physics: October 24-November 18 2022.

Talk Schedule


Time Title Speaker Location
9:00am Breakfast N/A SCGP Cafe
9:30am Numbers from quantum field theory Karen Yeats SCGP 102
10:30am Coffee Break N/A SCGP Cafe
11:00am Amplitudes and the Riemann Zeta Function Grant Remmen SCGP 102/ZOOM
12:00pm Lunch N/A SCGP Cafe
1:15pm Sums of certain arithmetic functions over Fq[T] and symplectic and orthogonal distributions Matilde Lalin SCGP 102
2:15pm Break N/A SCGP Cafe
2:30pm Euler Products and the Riemann Hypothesis Steve Gonek SCGP 102/ZOOM
3:30pm Tea N/A SCGP Cafe
4:00pm The recipe for moments of $L$-functions and characteristic polynomials of random matrices Sieg Baluyot SCGP 102