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.