# Partial Differential Equations and Analysis Seminar

No events are currently scheduled.

## Past events

07

Jan

2020

### Harmonic mean curvature flow and geometric inequalities »

In this talk, we use the harmonic mean curvature flow to prove Alexandrov-Fenchel type inequalities for strictly convex hypersurfaces in hyperbolic space.

10

Dec

2019

### Vector-valued time-frequency analysis and the bilinear Hilbert transform »

I will give an overview of how time-frequency analysis is used in proving these $L^p$-bounds, with focus on the recently understood setting of functions valued in UMD Banach spaces.

05

Nov

2019

### Global solutions to linear and semilinear Helmholtz and time-dependent Schr\"odinger equations »

A talk discussing recent work on solving the semilinear Helmholtz equation on Euclidean, or more generally asymptotically conic spaces.

15

Oct

2019

### On Escobar's conjecture and related topic »

The fundamental gap conjecture for Dirichlet eigenvalue problem on Euclidean domains is a well-known conjecture. In this talk we shall present our progress on Escobar's conjecture, namely, we confirm it for a large class of Riemannian manifolds, including Euclidean domains.

11

Oct

2019

### A priori estimates for Monge-Amp\`ere equation and applications. »

In this talk we will discuss the a priori estimates for some Monge-Amp\`ere type equation and their applications.

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.