Mathematics & Computer Science

Seminars and Colloquia

Thursday, October 30, 2014

04:15 pm - 05:15 pm

Math Colloquium, Ari Stern (Washington University in Stl Louis): "Simulating dynamical systems: classic methods and modern challenges"

Abstract: Ordinary differential equations (ODEs) are central to many areas of mathematics, and have a vast range of applications in science and engineering. However, most nonlinear ODEs cannot be solved in closed form. Fortunately, all hope is not lost: "numerical integrators" allow us to simulate these dynamical systems, obtaining approximate solutions to an arbitrary degree of accuracy. This talk will introduce a few classic methods for numerical integration, along with the theory used to analyze their stability and convergence. I will also discuss some recent research developments in the area of "geometric numerical integration," explaining why certain methods perform much better than others for simulating physical systems.

ESC 638

Friday, October 31, 2014

01:10 pm - 02:00 pm

Algebra Seminar, David Pollack (Wes): "A lifting theorem and computations towards an eigencurve for SL_3."

Abstract: Fix a prime p. We generalize our early method of computing overconvergent lifts of ordinary $p$-adic homology classes for SL_3 to allow computations of lifts of non-ordinary, but numerically non-critical classes. Then we will discuss an ongoing calculation to find to any desired degree of accuracy the germ of the projection to weight space of the eigencurve Z around the point z corresponding to the system of Hecke eigenvalues of this over convergent lift. We do this under the conjecturally mild hypothesis that Z is smooth at z.

ESC 618