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
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.
26
Mar
2019
Lower bound of the Riesz transform kernel on Stratified Lie groups, commutators and applications »
The commutator of the Riesz transform (Hilbert transform in dimension 1) and a symbol $b$ is bounded on $L^2(\mathbb R^n)$ if and only if $b$ is in the BMO space BMO$(\mathbb R^n)$ (Coifman--Rochberg--Weiss). It is natural to ask whether it holds for commutator of Riesz transform on Heisenberg groups.
22
Mar
2019
Axially asymmetric traveling fronts in balanced bistable reaction-diffusion equations »
For a balanced bistable reaction-diffusion equation, an axisymmetric traveling front has been well known. We prove that an axially asymmetric traveling front with any positive speed does exist in a balanced bistable reaction-diffusion equation.
19
Mar
2019
The marked length spectrum of Anosov manifolds »
We show some new rigidity result for the marked length spectrum of closed negatively curved manifolds.
05
Mar
2019
Eigenvalues of Schrödinger operators with complex valued potentials in $L^p$ »
I will speak on work of Rupert Frank and collaborators on eigenvalues of the Schrodinger operator consisting of the Laplacian on $R^d$ plus a complex valued, $L^p$ potential, and my work with Guillarmou and Krupchyk on a generalization to asymptotically conic manifolds.
28
Aug
2018
Sharp local smoothing estimates for Fourier integral operators »
PDE/Analysis Seminar
21
Aug
2018
Semiclassical resolvent estimates and wave decay in low regularity »
PDE/Analysis Seminar
07
Aug
2018
The square functional calculus »
This is our usual PDE/Analysis seminar
03
Apr
2018
The Kato Square Root Problem for Divergence Form Operators with Potential »
The Kato square root problem for divergence form elliptic operators is the equivalence statement $\norm{\sqrt{- \mathrm{div} \br{A \nabla}}u} \simeq \norm{\nabla u}$, where $A$ is a complex matrix-valued function.
12
Feb
2018
Optimal transportation between unequal dimensions »
In the last few decades, the theory of optimal transportation has blossomed into a powerful tool for exploring applications both within and outside mathematics.
05
Dec
2017
Sparse dominations and sharp weighted estimates for singular integral operators »
We shall discuss the concept of sparse dominations of singular integral operators, in particular for those operators whose kernel do not satisfy any regularity estimate.
28
Nov
2017
Ritt property and functional calculus of subordinated operators in the group case »
This is joint work with Christian Le Merdy.