Introduction
This year’s lecture by Nalini Anantharaman will focus on the universal behaviors of spectra studied in physics and mathematics. Faced with the difficulty of explicitly calculating spectra, physicist E. Wigner proposed a statistical approach: highlighting widespread phenomena rather than focusing on individual details. Wigner postulated a simple probabilistic model that, surprisingly, agrees well with frequently observed spectral statistics (nuclei of large atoms, quantum “billiards,” graphs, etc.). We will present recent advances that support the validity of this model, while attempting to draw a connection to the concept of a “chaotic system.”