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Partial Differential Equations and Analysis Seminar
The partial differential equations and analysis seminar is the research seminar associated with the applied and nonlinear analysis, and the analysis and geometry programs.
No events are currently scheduled.
Past events
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.
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.
