# Research

## Analysis

### Friday, December 4, 2020

Title: The clamped plate problem and function theory, Part III (The Grand Finale)
Speaker: Dima Khavinson
Time: 4:00pm–5:00pm
Place: Microsoft Teams

### Friday, November 20, 2020

Title: The clamped plate problem and function theory, Part II
Speaker: Dima Khavinson
Time: 4:00pm–5:00pm
Place: Microsoft Teams

### Friday, November 13, 2020

Title: The clamped plate problem and function theory
Speaker: Dima Khavinson
Time: 4:00pm–5:00pm
Place: Microsoft Teams

#### Abstract

If the weight is distributed over an elastic plate with clamped edge, will the plate go down at every point inside?

J. Hadamard in 1908 conjectured that the answer is probably “Yes” at least for convex plates. In fact, the answer in general is “No”. We shall discuss this problem and why it has become crucially important for classical function theory in the 1990s and its connection with the reproducing kernels. Plenty of open problems remain. This is ajoint project with C. Bénéteau and A. Sola.

### Friday, November 6, 2020

Title: Asymptotics of oscillatory matrix Riemann-Hilbert problems by dbar-steepest descent method, Part III
Speaker: Fudong Wang
Time: 4:00pm–5:00pm
Place: Microsoft Teams

### Friday, October 30, 2020

Title: Asymptotics of oscillatory matrix Riemann-Hilbert problems by dbar-steepest descent method, Part II
Speaker: Fudong Wang
Time: 4:00pm–5:00pm
Place: Microsoft Teams

### Friday, October 23, 2020

Title: Asymptotics of oscillatory matrix Riemann-Hilbert problems by dbar-steepest descent method
Speaker: Fudong Wang
Time: 4:00pm–5:00pm
Place: Microsoft Teams

#### Abstract

We will discuss the asymptotic behavior of a certain type of oscillatory $$2\times 2$$ matrix Riemann-Hilbert problems (RHP) arising in the AKNS hierarchy. We will first review the inverse scattering transform and $$L^2$$ RHP theory. Then, we will discuss a general scheme of applying the dbar-steepest descent method to solve the asymptotic problem. The results can be directly applied to study the long-time asymptotic behavior of the nonlinear Schrödinger equation, the modified KdV equation and their higher-order generalization. This talk is based on my dissertation work.

### Friday, October 16, 2020

Title: Around a Theorem of F. Dyson and A. Lenard: Some Neat Results from Electrostatics, Part III
Speaker: Nathan Hayford
Time: 4:00pm–5:00pm
Place: Microsoft Teams

### Friday, October 9, 2020

Title: Around a Theorem of F. Dyson and A. Lenard: Some Neat Results from Electrostatics, Part II
Speaker: Nathan Hayford
Time: 4:00pm–5:00pm
Place: Microsoft Teams

### Friday, October 2, 2020

Title: Around a Theorem of F. Dyson and A. Lenard: Some Neat Results from Electrostatics
Speaker: Nathan Hayford
Time: 4:00pm–5:00pm
Place: Microsoft Teams

#### Abstract

We discuss a collection of interesting results from potential theory/electrostatics, with plenty of historical exposition, wherever possible. These results include Onsager’s inequality, some necessary conditions for equilibrium of a distribution of charge, and result on degeneracy in the celebrated “Maxwell’s Problem”. We also mention a few related open problems, if time permits. This talk is based on a recent(-ish) paper with A. Abanov, D. Khavinson, and R. Teodorescu.

### Friday, September 25, 2020

No seminar this week.