R A N D O M    M A T R I C E S     A N D     N U M B E R     T H E O R Y ,    F a l l  2 0 1 2 

Lectures: Tuesday and Thursday, 11.30-1pm, in Science Center 101b.

Lecturer: Paul Bourgade, office hours Tuesday 5-6pm, you also can email me (bourgade@math.harvard.edu) to set up an appointment or just drop by (Science Center 341).

Course assistant: Jeffrey Kuan (jkuan@math.harvard.edu).

Lecture notes available here, weekly updated. Please let me know about the inaccuracies and typos you will certainly find.

Course description: an introduction to random matrices, emphasizing how related statistics occur in analytic number theory (spacings between large zeros, moments, low-lying zeros of L-functions).

Prerequisites: probability theory and complex analysis.

Textbooks: for the random matrices part, a reference is Anderson, Guionnet, Zeitouni, An introduction to random matrices. For the number theoretic part, a reference is Montgomery, Vaughan, Multiplicative Number Theory I: Classical Theory.

A tentative schedule for this course is: