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.

PDE/Analysis Seminar

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.

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.