The unreasonable effectiveness of dynamics in number theory

Series
Research Horizons Seminar
Time
Wednesday, October 22, 2025 - 12:30pm for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Asaf Katz – Georgia Tech – akatz47@gatech.eduhttps://sites.google.com/view/asafkatz
Organizer
Yanbo Wang, Xinlin Wu

I will discuss several classical problems in number theory about representation of numbers and forms by quadratic forms and related counting results. We will describe several applications such as pair correlations and eigenvalue statistics for quantum systems.
Then we will move to related problems about irrational forms, such as the Oppenheim conjecture and explain how homogeneous dynamics can help to tackle such problems.
The talk will be self contained and hopefully accessible.