# Partial Differential Equations and Analysis Seminar

## Upcoming events

10

Dec

2019

10–11am 10 December 2019

Dr. Alex Amenta, Universität Bonn (Germany)

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.

## Past events

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.

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.