## Free Probability & Random Matrices Seminar

### Tuesday, January 16th, 2018

**Time:** 4:00-5:30 p.m. **Place:** Jeffery Hall 319

**Speaker:** Neha Prabu

**Title:** Semicircle distribution in number theory

**Abstract:** In free probability theory, the role of the semicircle distribution is analogous to that of the normal distribution in classical probability theory. However, the semicircle distribution also shows up in number theory: it governs the distribution of eigenvalues of Hecke operators acting on spaces of modular cusp forms. In this talk, I will give a brief introduction to this theory of Hecke operators and sketch the proof of a result which is a central limit type theorem from classical probability theory, that involves the semicircle measure.

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