Department of

Mathematics


Seminar Calendar
for events the day of Wednesday, January 25, 2006.

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Wednesday, January 25, 2006

3:00 pm in 343 Altgeld Hall,Wednesday, January 25, 2006

Quantum mechanics: the harmonic oscillator

Sheldon Katz   [email] (UIUC Math and Physics)

Abstract: Having established some language for several formulations of quantum mechanics last time, I will focus on the formalism of canonical quantization, illustrating with the harmonic oscillator. If time allows, the path integral formalism will make a brief reappearance at the end. The talk is structured so that attendance at the first meeting will not be essential.

4:00 pmWednesday, January 25, 2006

4:00 pm in 245 Altgeld Hall,Wednesday, January 25, 2006

Shortwave instabilities of ideal fluid and the cocycle theory

Roman Shvydkoy (University of Illinois at Chicago)

Abstract: Shortwave instabilities of an ideal fluid flow are instabilities generated by highly oscillating localized wavepackets, which propagate according to a finite-dimensional system of ODEs. Analysis of the cocycle (fundamental matrix solution) generated by this system of ODEs establishes an equivalence relation between the essential spectrum of the linearized Euler equation and all possible shortwave instabilities that can occur in a given steady flow. Thus, studying the essential spectrum of the Euler equation we can understand more about how an ideal fluid can get unstable. We will survey various results that have been obtained via the cocycle approach. Those include inherent instability of 3D flows with periodic streamlines, pseudo-differential structure of the Euler and Navier-Stokes semigroups, spectrum under vanishing viscosity limit. We will show that typically the essential spectrum of the Euler equation is a vertical solid band or a ladder. Host: V. Zharnitsky