Research Seminars @ Illinois

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Tailored for undergraduate researchers, this calendar is a curated list of research seminars at the University of Illinois. Explore the diverse world of research and expand your knowledge through engaging sessions designed to inspire and enlighten.

To have your events added or removed from this calendar, please contact OUR at ugresearch@illinois.edu

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)

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Originating Calendar

General Events - Department of Mathematics

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.

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