Mathematics Colloquia, Fall 2020

September 3, 2020

4:00 p.m., 245 Altgeld Hall
Speaker: Marius Junge, University of Illinois at Urbana-Champaign
Title: TBA
Abstract: To come.

 

September 10, 2020

4:00 p.m., via Zoom (please contact Jozsef Balogh)
Speaker: Noga Alon (Princeton University and Tel Aviv)
Title: Fair representation
Hosts: Jozsef Balogh and Alexandr Kostochka
Abstract: A substantial number of results and conjectures deal with the existence of a set of prescribed type which contains a fair share from each member of a finite collection of objects in a space. Examples include the Ham-Sandwich Theorem in Measure Theory, the Hobby-Rice Theorem in Approximation Theory, the Necklace Theorem and the Ryser Conjecture in Discrete Mathematics, and more. The techniques in the study of these results combine combinatorial, topological, geometric and algebraic tools. I will describe the topic, focusing on several recent results.

 

October 22, 2020

4:00 p.m., 245 Altgeld Hall
Speaker: Ralf Hiptmair (ETZ Zurich)
Title: TBA
Host: Anil Hirani
Abstract: To come.
 

November 5, 2020

4:00 p.m., via Zoom (please contact Alex Yong for information)
Speaker: Greta Panova (University of Southern California)
Title: TBA
Host: Alex Yong
Abstract: To come 
 

December 3, 2020

4:00 p.m., via Zoom 
Speaker: Mikhail Ostrovskii
Title: TBA
Hosts: Marius Junge, Denka Kutzarova
Abstract: To come 

 

Date TBA

4:00 p.m., 245 Altgeld Hall
Speaker: Andrew Granville (University of Montreal)
Title: TBA
Host: Kevin Ford
Abstract: To come
 

Date TBA

4:00 p.m., 245 Altgeld Hall
Speaker: Bjorn Sandstede (Brown University)
Title: TBA
Host: Jared Bronski
Abstract: To come
 

Date TBA

4:00 p.m., 245 Altgeld Hall
Speaker: Kevin Zumbrun (Indiana University Bloomington)
Title: Stability of roll wave solutions in inclined shallow-water flow
Host: Vera Hur
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.
 

Date TBA

4:00 p.m., 245 Altgeld Hall
Speaker: Jared Wunsch (Northwestern University)
Title: Trapping, resonances, and the decay of waves
Host: Pierre Albin
Abstract: I will discuss some results, new and old, involving the influence of the geometry on the decay of waves.  The quantum correspondence principle dictates that at high frequency, the dynamics of particle trajectories should be related to the rate at which the energy of a solution to the wave or Schrödinger equation decays.  This relationship is mediated by the existence of resonances, which correspond to states with a finite (but possibly long) lifetime that ultimately decay owing to tunneling effects.  I will discuss what we know about the existence and nonexistence of resonances, and focus on some recent results about resonances associated to the subtle effects of diffraction in classical and quantum problems that have singular structures in a metric or potential.
 

Date TBA

4:00 p.m., 245 Altgeld Hall
Speaker: Kevin Purbhoo (University of Waterloo)
Title: To be announced
Host: Alex Yong
Abstract: To come
 

Date TBA

4:00 p.m., 245 Altgeld Hall
Speaker: Elizabeth Meckes (Case Western Reserve University)
Title: To be announced
Hosts: Pierre Albin
Abstract: To come
 

Date TBA

4:00 p.m., 245 Altgeld Hall
Speaker: Sami Assaf (University of Southern California)
Title: To be announced
Host: Alex Yong and Reuven Hodges
Abstract: To come