Title: Extension and Regularity of CR Functions near CR Singularities
Abstract:
CR functions are certain generalizations of holomorphic functions and CR
manifolds are those that support CR functions. For instance, a
pseudoconvex hypersurface in $\mathbb{C}^N$ is a CR manifold and CR
functions are locally boundary values of holomorphic functions. We will
begin by describing this holomorphic extension result before proceeding to
discuss the codimension two case. Codimension two submanifolds of
$\mathbb{C}^N$ generically have isolated CR singularities and we are
interested in studying the behaviour of the extension of CR functions near
CR singularities. We prove that under certain nondegeneracy conditions on
the CR singularity this extension is smooth up to the CR singularity. This
is joint work with Jiri Lebl and Alan Noell.
5:00pm
6:00pm
Time:
4:00pm-6:30pm
Location:
Room 216, Department of Mathematics
Description:
Title: Local Fields
Abstract: This is the first in a series of lectures on class field theory.
We begin with Chapter 1 in Cassels and Frohlich.
Time:
4:00pm-5:00pm
Location:
Ramanujan Hall
Description:
Title: Extension and Regularity of CR Functions near CR Singularities
Abstract:
CR functions are certain generalizations of holomorphic functions and CR
manifolds are those that support CR functions. For instance, a
pseudoconvex hypersurface in $\mathbb{C}^N$ is a CR manifold and CR
functions are locally boundary values of holomorphic functions. We will
begin by describing this holomorphic extension result before proceeding to
discuss the codimension two case. Codimension two submanifolds of
$\mathbb{C}^N$ generically have isolated CR singularities and we are
interested in studying the behaviour of the extension of CR functions near
CR singularities. We prove that under certain nondegeneracy conditions on
the CR singularity this extension is smooth up to the CR singularity. This
is joint work with Jiri Lebl and Alan Noell.