# Partial Differential Equations and Analysis Seminar

No events are currently scheduled.

## Past events

24

Sep

2019

### On $L_2$-uniqueness of symmetric diffusion equations »

We discuss the uniqueness of solutions of the parabolic evolution equation $\partial\varphi/\partial t+H\varphi=0$ where $H=-\mathrm{div}(C\nabla)$ is a second-order degenerate elliptic operator acting on a domain $\Omega$ in $\mathbf{R}^d$.

17

Sep

2019

### Riesz transforms on a class of non-doubling manifolds II »

We consider L^p boundedness of the Riesz transform on a class of non-doubling manifolds obtained by taking the connected sum of two Riemannian manifolds which are both a product of a Euclidean space and a closed manifold.

27

Aug

2019

### Special Lagrangian equations & Optimal transport for dendritic structures »

In this seminar, Professor Yu Yuan and Professor Young-Heon Kim will discuss special lagrangian equations and optimal transport for dendritic structures.

27

Aug

2019

### Special Lagrangian equations & Optimal transport for dendritic structures »

In this seminar, Professor Yu Yuan and Professor Young-Heon Kim will discuss special lagrangian equations and optimal transport for dendritic structures.

16

Aug

2019

### Geometry of Ricci solitons »

In this seminar, Professor Huai-Dong Cao will discuss some recent progress on Ricci solitons, especially in dimension four.

13

Aug

2019

### A new phenomenon involving inverse curvature flows in hyperbolic space »

In this seminar, we discover a new phenomenon involving inverse curvature flows in hyperbolic space.

09

Aug

2019

### Dynamics of a Fisher-KPP nonlocal diffusion model with free boundaries »

Professor Yihong Du will introduce and discuss a class of free boundary problems with "nonlocal diffusion".

06

Aug

2019

### Energy critical 2-D stochastic wave equation »

In this seminar, Nimit Rana will prove the existence and uniqueness of a local maximal solution to a $H^1$-critical stochastic wave equation with multiplicative noise on a smooth bounded domain $\mathcal{D} \subset \mathbb{R}^2$ with exponential nonlinearity.

09

Jul

2019

### The perfectly matched layer (PML): theory and practice »

In this talk we discuss the well-posedness and stability of the PML initial boundary value problem. In particular, we will perform a spectral analysis of the integro-differential operator corresponding to the PML-IBVP, and derive general solutions of the PML-IBVP in the Fourier- Laplace domain.

11

Jun

2019

### Bounds on the maximal Bochner-Riesz means for elliptic operators »

I will discuss $L^p$ boundedness of the maximal Bochner-Riesz means for self-adjoint operators of elliptic type which satisfy
the finite speed of propagation for the associated wave operator.

04

Jun

2019

### Weyl Pseudodifferential Operators in Ornstein-Uhlenbeck Settings »

The classical Weyl pseudodifferential calculus is a particular choice of "quantisation". Ornstein-Uhlenbeck (OU) operators are analogs of the Laplacian adapted to spaces with Gaussian measure. I will explain my current work in adapting the Weyl calculus to the OU setting.

28

May

2019

### On square functions in the control of linear systems »

I will survey some fundamental concepts in linear systems.

17

May

2019

### Disclinations in 3D Landau-de Gennes theory »

In this talk I will introduce a new bifurcation theory to find multiple solutions of Landau-de Gennes equation.

14

May

2019

### Spaces of functions invariant under Fourier integral operators of order zero (part 2) »

This talk follows up on the seminar by Andrew Hassell on May 8. However, at the start of my talk I will recall the contents of his seminar, so that the talk is accessible without prior knowledge of the subject.

07

May

2019

### Spaces of functions invariant under Fourier integral operators of order zero »

It was proved by Seeger, Sogge and Stein that Fourier Integral operators (FIOs) in $n$ dimensions map
the Hardy space $H^1$ into $L^1$ provided they have sufficiently negative order, that is, no bigger than $-(n-1)/2$.