# 2012 Chern Lectures

**The 2012 Chern Lectures** were given by **Jean Bourgain**, of the Institue of Advanced Studies, on April 10th, 12th, 17th, and 19th.

**Series title:** Group expansion,spectral gaps and applications**Lecture 1:**

Tuesday, April 10, 2012

4:00 pm - 5:00 pm, Room 1, LeConte Hall

The
notion of expander families; Selberg's theorem on congruence Cayley
graphs of SL2(Z), the Lubotzky-Weiss conjecture and the present state of
the art. *A dinner in honor of the speaker will be held on
Tuesday, April 10 at 6:30 pm at Venezia Restaurant, 1799 University Av.
Open to all.**Please inquire about special pricing. To sign up please send an email to chorin [at] math [dot] berkeley [dot] edu.***Lecture 2:**

Thursday, April 12, 2012

4:00 pm - 5:00 pm, Room 60, Evans Hall

Spectral
gaps; hyperbolic lattice point counting, Lax-Phillips theory and the
thermodynamical approach;first arithmetical applications to prime number
sieving in the orbits of thin groups.**Lecture 3:**

Tuesday, April 17, 2012

4:00 pm - 5:00 pm, Room TBA

Diophantine
applications; curvatures in Apollonian circle packings and Zaremba's
conjecture on continued fraction expansions, finiteness in arithmetic
geometry.**Lecture 4:**

Thursday, April 19, 2012

4:00 pm - 5:00 pm, Room 60, Evans Hall

Spectral
gaps in Lie groups; the unitary group and applications to quantum
computation and stochastic tilings; SL2 (R) and its relevance to
questions in computer science and the theory of random matrix products.