Columbia Mathematics Department Colloquium

Columbia University Mathematics Colloquium

Fall 2003

Columbia Mathematics Department Colloquium meets in Math 520 every two to three weeks on Wednesday afternoons at 4:15, and is preceded by tea at 3:45. Colloquiua are of general mathematical interest and aimed at both faculty and graduate students.

Spring 2004 Schedule

Sept. 17 Peter Li - University of California, Irvine Complete manifolds with positive spectrum

Oct. 15

Yuri Tschinkel - Universität Göttingen

On the arithmetic of K3 surfaces
Abstract: I will explain some results and constructions on K3 surfaces over countable fields.

Nov. 12 Frank Merle - Université de Cergy-Pontoise & IAS Understanding formation of singulatity in critical nonlinear Schrodinger equations

Dec. 3

Ken Ono - Wisconsin- Madison

Class groups and elliptic curves
Abstract: We consider questions related to the arithmetic of elliptic curves and quadratic number fields, two of the most basic objects in algebraic number theory and arithmetic geometry. We shall survey classical questions of Gauss, Cohen and Lenstra, Goldfeld, and Mazur on the `expected' behavior of ideal class groups, Mordell-Weil groups, and Shafarevich-Tate groups. The purpose of this lecture is to review these fundamental questions and to present recent results.

Organizer: Panagiota Daskalopoulos.

Sept. 17	Peter Li - University of California, Irvine	Complete manifolds with positive spectrum
Oct. 15	Yuri Tschinkel - Universität Göttingen	On the arithmetic of K3 surfaces Abstract: I will explain some results and constructions on K3 surfaces over countable fields.
Nov. 12	Frank Merle - Université de Cergy-Pontoise & IAS	Understanding formation of singulatity in critical nonlinear Schrodinger equations
Dec. 3	Ken Ono - Wisconsin- Madison	Class groups and elliptic curves Abstract: We consider questions related to the arithmetic of elliptic curves and quadratic number fields, two of the most basic objects in algebraic number theory and arithmetic geometry. We shall survey classical questions of Gauss, Cohen and Lenstra, Goldfeld, and Mazur on the `expected' behavior of ideal class groups, Mordell-Weil groups, and Shafarevich-Tate groups. The purpose of this lecture is to review these fundamental questions and to present recent results.