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.

In this talk I will introduce a new bifurcation theory to find multiple solutions of Landau-de Gennes equation.

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 $-(n-1)/2$.

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.

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

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.

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.