- Series
- Number Theory
- Time
- Wednesday, October 21, 2026 - 3:30pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Alexey Pozdnyakov – Princeton University – ap5763@princeton.edu – https://www.math.princeton.edu/people/alexey-pozdnyakov
- Organizer
- Cruz Castillo
Murmurations were first observed as surprising correlations between Frobenius traces and root numbers of elliptic curves. They were then rigorously established for the family of modular forms in the level aspect by Zubrillina, and have since been studied in many families of L-functions in the number field setting. As pointed out by Sarnak, murmurations can also be interpreted as a phase transition in the one-level density of the low-lying zeros of the family. The goal of this talk is to investigate the function field analogue of this phenomenon. We will compute the murmuration density for the family of quadratic characters, relate the mean of the murmuration density to the stable homology of the moduli space of hyperelliptic curves, and clarify the relationship this has to one-level density. As a corollary, we will also obtain non-vanishing results for the L-functions of these curves. This is joint work with Lalín, Lee, and Oliver.