Expanders: from arithmetic to combinatorics and back


Alexander Gamburd

University of California, Santa Cruz

Northeastern University

Thursday, September 17, 2009


Talk at 4:30 p.m. in 509 Lake Hall

Tea at 4:00 p.m. in 544 Nightingale Hall


Abstract:   Expanders are highly-connected sparse graphs widely used in computer science. The optimal expanders -- Ramanujan graphs -- were constructed using deep results from the theory of automorphic forms. In recent joint work with Bourgain and Sarnak tools from additive combinatorics were used to prove that a wide class of "congruence graphs" are expanders; this expansion property plays crucial role in establishing novel sieving results pertaining to primes in orbits of linear groups.

Here are some directions to Northeastern University. Lake Hall and Nightingale Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street. The two halls are connected, with no well-defined boundary in between. In particular, 509 Lake Hall is on the same corridor as 544 Nightingale Hall.

There is free parking available for people coming to the Colloquium at Northeastern's visitor parking (Rennaisance Garage). The entrance is from Columbus Avenue. If coming by car, you should park there and take the parking talon. After the lecture, you may pick up the payment coupon from Andrei Zelevinsky.

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Posted:: August 28, 2009    URL: