Arithmetic Statistics, Automorphic Forms and Ergodic Methods

ag.algebraic-geometry ds.dynamical-systems nt.number-theory
Start Date
2023-04-24 
End Date
2023-04-28 
Institution
Max Planck Institute for Mathematics 
City
Bonn 
Country
Germany 
Meeting Type
conference 
Homepage
https://www.mpim-bonn.mpg.de/node/11531 
Contact Name
 

Description

The field of arithmetic statistics is a fast-moving area of number theory, dealing with distributional results for many basic and important objects: ranks of elliptic curves, central values of L-functions, number fields, modular symbols, orbits of discrete groups etc. The techniques involved come from diverse areas of mathematics e.g. automorphic forms, ergodic theory, spectral theory, dynamical systems, probabilistic number theory, representation theory and random matrix theory. This workshop intends to bring together researchers of all career levels to present their work and exchange ideas and techniques on arithmetic statistics. Motivated by the programme of Mazur and Rubin based on their computational study of elliptic curves over abelian extensions of fixed degree, the meeting will focus on modular symbols, Manin's noncommutative modular symbols, equidistribution of lattice points on the sphere, Heegner points, and closed geodesics, including the error term in the Prime Geodesic Theorem.

There will be invited talks lasting 50 or 25 minutes and other events aimed at facilitating discussions among participants.

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