Events for 11/02/2009 from all calendars

Algebraic Geometry Seminar

Time: 3:00PM - 4:00PM

Location: MILN 216

Speaker: Erwan Brugallé, Institut de Mathématiques de Jussieu

Title: Tropical inflection points of tropical plane curves

Abstract:

I will define what is a tropical inflection point of a tropical plane curve, and explain how this notion is related to inflection points of complex algebraic plane curves. As an application, I will show that there exist maximal plane real algebraic curves of any degree with the maximal number of real inflection points allowed by the Klein Formula.

A crucial tool in our approach is the use of tropical modifications. If time permits, I will give other examples of applications of this powerful tool.

(This is joint work with Lucia Lopez de Medrano.)

URL: Link

Graduate Tea

Time: 3:30PM - 4:00PM

Location: Blocker 627

Applied Math Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 627

Speaker: Dr. Vit Prusa, Charles University, Prague

Title: Stability of Oscillating Pipe Flow

Abstract: Stability of (steady) pipe flow is a classical problem in fluid mechanics that dates back to Reynolds' experiments done in 1883. Although one can easy find a solution to the governing equations (the Navier--Stokes equations)---the parabolic velocity profile---this solution can be, in a real experiment, observed only for certain values of the Reynolds number. If the Reynolds number is higher that a certain critical value, the unidirectional laminar flow ceases to exist and the flow becomes "turbulent". The question is to find the value of the critical Reynolds number that marks transition from laminar to turbulent flow and (maybe equivalently) loss of stability of the laminar flow. In the first part of the talk I will discuss several classical approaches to the problem and their limitations, and then I will present some new results concerning (mainly) the oscillating pipe flow. At the end I will briefly comment some promising recent approaches to the problem that are based on "numerical experiments", and that call for more rigorous mathematical treatment.