Mathematics Colloquium

Department of Mathematics
Seminars

Address: Mathematics 253-37 | Caltech | Pasadena, CA 91125
Telephone: (626) 395-4335 | Fax: (626) 585-1728

Mathematics Colloquium
2011 - 2012

Tuesday, January 31, 2012
4:00 p.m. // 151 Sloan
Zhiwei Yun (MIT)

Geometry and the Inverse Galois Problem

Abstract:

We will use geometric methods to solve new cases of the inverse Galois problem: we will show that certain finite simple groups of Lie type (including E_8) appear as Galois groups over Q.

Wednesday, January 25, 2012
4:00 p.m. // 151 Sloan
Goncalo Tabuada (MIT)

Noncommutative Motives

Abstract:

TBA

Tuesday, November 15, 2011
4:15 p.m. // 151 Sloan
Alexander Sodin (Institute for Advanced Study)

Random band matrices (a survey)

Abstract:

We shall discuss the main conjectures pertaining to random band matrices, and describe the results obtained so far. We focus on the following two approaches:

1) via a perturbative expansion in the inverse powers of the band width,
2) via a supersymmetric functional integral.

Thursday, November 10, 2011
4:15 p.m. // 151 Sloan
Rupert Frank (Princeton University)

Sharp constants in inequalities on the Heisenberg group

Abstract:We derive the sharp constants for the inequalities on the Heisenberg group whose analogues on Euclidean space are the well known Hardy-Littlewood-Sobolev inequalities. From these inequalities we obtain the sharp constants for their duals, which are the Sobolev inequalities for the Laplacian and conformally invariant fractional Laplacians. Only one special case had been known previously, due to Jerison-Lee more than twenty years ago, which was crucial in the solution of the CR Yamabe problem. Our methodology is completely different from that used to obtain the Euclidean inequalities and can be used to give a new, rearrangement free, proof of the HLS inequalities.

The talk is based on joint work with E. H. Lieb.

Tuesday, November 8, 2011
4:15 p.m. // 151 Sloan
Nets Katz (University of Indiana)

Erdös' distinct distances problem in the plane

Abstract: In joint work with L. Guth, we show that there is a universal constant C > 0 so that any set of N points in the plane determines at least {N\overClogN} distinct distances. This settles a longstanding problem of Erdös regarding the best exponent of N that one can obtain in that estimate.