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Distribution results play an increasingly important role in number theory. The aim of this winter school is to give an introduction to Random Matrix Theory and Number Theory. The necessary background on probability theory, random matrices, Zeta Functions and L-functions will be given. After providing the necessary background, we will introduce the Montgomery-Odlyzko law relating the distribution of zeros of the Riemann zeta function to the disitribution of eigenvalues of random Hermitian matrices. We will also present several examples of recent distribution results from in families of curves over finite fields and number fields.

Aycan Şahin: aycansahin@nesinvakfi.org