PDE Geometric Analysis seminar

The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.

Seminar Schedule Spring 2013

date	speaker	title	host(s)
February 4	Myoungjean Bae (POSTECH)	Transonic shocks for Euler-Poisson system and related problems	Feldman
February 18	Mike Cullen (Met. Office, UK)	Modelling the uncertainty in predicting large-scale atmospheric circulations.	Feldman
March 18	Mohammad Ghomi(Math. Georgia Tech)	Tangent lines, inflections, and vertices of closed curves.	Angenent
April 8	Reserved		Feldman
May 5	Diego Cordoba (Madrid)	TBA	Kiselev

Abstracts

Myoungjean Bae (POSTECH)

Transonic shocks for Euler-Poisson system and related problems

Abstract: Euler-Poisson system models various physical phenomena including the propagation of electrons in submicron semiconductor devices and plasmas, and the biological transport of ions for channel proteins. I will explain difference between Euler system and Euler-Poisson system and mathematical difficulties arising due to this difference. And, recent results about subsonic flow and transonic flow for Euler-Poisson system will be presented. This talk is based on collaboration with Ben Duan and Chunjing Xie.

Mike Cullen (Met. Office, UK)

Modelling the uncertainty in predicting large-scale atmospheric circulations

Abstract: This talk describes work on quantifying the uncertainty in climate models by using data assimilation techniques; and in estimating the properties of large-scale atmospheric flows by using asymptotic limit solutions.

Mohammad Ghomi(Math. Georgia Tech)

>> Abstract: We show that every smooth closed curve C immersed in Euclidean 3-space satisfies the sharp inequality 2(P+I)+V >5 which relates the numbers P of pairs of parallel tangent lines, I of inflections (or points of vanishing curvature), and V of vertices (or points of vanishing torsion) of C. The proof, which employs curve shortening flow with surgery, is based on corresponding inequalities for the numbers of double points, singularities, and inflections of closed curves in the real projective plane and the sphere which intersect every closed geodesic. These findings extend some classical results in curve theory including works of Moebius, Fenchel, and Segre, which is also known as Arnold's ``tennis ball theorem".