# Partial Differential Equations and Analysis Seminar

## Upcoming events

27

Aug

2019

1.30–3.30pm 27 August 2019

Professor Yu Yuan (MSRVP), University of Washington, Professor Young-Heon Kim, University of British Columbia

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

1.30–3.30pm 27 August 2019

Professor Yu Yuan (MSRVP), University of Washington, Professor Young-Heon Kim, University of British Columbia

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

## Past events

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 $-(n-1)/2$.

16

Apr

2019

### In memory of Alan McIntosh and Joe Moyal: an operator theoretic approach to pseudo-differential calculus »

Can one use pseudo-differential calculus in situations where no Fourier transform is available? On a manifold, one can use the euclidean pseudo-differential calculus locally, but can one find a global analogue?

09

Apr

2019

### Adapted sparse domination and good-lambda inequalities »

The method of sparse domination is an efficient technique for obtaining weighted L^p bounds of singular integral operators with sharp dependence on the weight constant. In this talk we show how one can use good-lambda inequalities to obtain a sparse domination that is adapted to various operators and weight classes.

02

Apr

2019

### On the global dynamics of Maxwell-Klein-Gordon equations »

It is conjectured that for the Maxwell-Klein-Gordon equations having data with non-vanishing charge and arbitrary large size, the global solutions disperse as linear waves and enjoy the so-called peeling properties for pointwise estimates. We give a gauge independent proof of the conjecture.

29

Mar

2019

### Compactification of Lie Groups »

I will discuss compactifications of semisimple Lie groups, in particular SU(n) over the real and complex fields, as manifolds with corners.