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The clamped plate problem and function theory, Part III (The Grand Finale)

Dima Khavinson

4:00pm–5:00pm

Microsoft Teams

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The clamped plate problem and function theory, Part II

Dima Khavinson

4:00pm–5:00pm

Microsoft Teams

**Title**

**Speaker**

**Time**

**Place**

The clamped plate problem and function theory

Dima Khavinson

4:00pm–5:00pm

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.

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Asymptotics of oscillatory matrix Riemann-Hilbert problems by dbar-steepest descent method, Part III

Fudong Wang

4:00pm–5:00pm

Microsoft Teams

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**Speaker**

**Time**

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Asymptotics of oscillatory matrix Riemann-Hilbert problems by dbar-steepest descent method, Part II

Fudong Wang

4:00pm–5:00pm

Microsoft Teams

**Title**

**Speaker**

**Time**

**Place**

Asymptotics of oscillatory matrix Riemann-Hilbert problems by dbar-steepest descent method

Fudong Wang

4:00pm–5:00pm

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.

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Around a Theorem of F. Dyson and A. Lenard: Some Neat Results from Electrostatics, Part III

Nathan Hayford

4:00pm–5:00pm

Microsoft Teams

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Around a Theorem of F. Dyson and A. Lenard: Some Neat Results from Electrostatics, Part II

Nathan Hayford

4:00pm–5:00pm

Microsoft Teams

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**Speaker**

**Time**

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Around a Theorem of F. Dyson and A. Lenard: Some Neat Results from Electrostatics

Nathan Hayford

4:00pm–5:00pm

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.

No seminar this week.