Department of

Mathematics


Seminar Calendar
for events the day of Thursday, March 12, 2020.

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Thursday, March 12, 2020

2:00 pm in 347 Altgeld Hall,Thursday, March 12, 2020

Tracy-Widom distribution and spherical spin glass (Part II)

Qiang Wu (UIUC Math)

Abstract: I will talk about the connection between spherical spin glass(SSK) and random matrices, in particular, the fluctuation of free energy in SSK on low temperatures regime is given by GOE Tracy-Widom distribution.

4:00 pm in 245 Altgeld Hall,Thursday, March 12, 2020

Stability of roll wave solutions in inclined shallow-water flow

Kevin Zumbrun   [email] (Indiana University Bloomington)

Abstract: We review recent developments in stability of periodic roll-wave solutions of the Saint Venant equations for inclined shallow-water flow. Such waves are well-known instances of hydrodynamic instability, playing an important role in hydraulic engineering, for example, flow in a channel or dam spillway. Until recently, the analysis of their stability has been mainly by formal analysis in the weakly unstable or ``near-onset'' regime. However, hydraulic engineering applications are mainly in the strongly unstable regime far from onset. We discuss here a unified framework developed together with Blake Barker, Mat Johnson, Pascal Noble, Miguel Rodrigues, and Zhao Yang for the study of roll wave stability across all parameter regimes, by a combination of rigorous analysis and numerical computation. The culmination of our analysis is a complete stability diagram, of which the low-frequency stability boundary is, remarkably, given explicitly as the solution of a a cubic equation in the parameters of the solution space.