Colloquium
- Event Type
- Seminar/Symposium
- Sponsor
- Jared Bronski
- Location
- 165 Noyes; reception in 300 Harker at 3pm
- Date
- Dec 4, 2025 4:00 pm
- Speaker
- Gregotu Berkolaiko (Texas A&M University)
- Views
- 16
Title: Universality of nodal fluctuations: from quantum chaos to algebraic geometry.
Abstract: Quantum chaos is the study of signatures of chaotic dynamics at the quantum level. The objects of study include the energy (eigenvalue) or wavefunction (eigenfunction) statistics. Nodal fluctuations belong to the second class; they express deviations of the number of zeros (or nodal domains) of the eigenfunction from its expected value. We will discuss the nodal fluctuations in a particular model, discrete Schroedinger operators on graphs. The conjecture is that the nodal fluctuations are always Gaussian, in the appropriate limit and after appropriate normalization. While the conjecture has been established in some classes of graphs, it is mostly wide open. We will review recent progress in this area which combines many different approaches: Morse Theory, Random Matrices, Spectral Graph Theory and Algebraic Geometry.