#
Emerging applications of complexity for CR mappings

September 13 to September 17, 2010
at the

American Institute of Mathematics,
San Jose, California

organized by

John P. D'Angelo and Peter Ebenfelt

## Original Announcement

This workshop will focus on the
evolving notion of complexity in CR Geometry.
The basic set-up considers real hypersurfaces in complex Euclidean spaces
of different dimensions and the collection of CR maps between them. Many
of the ideas apply when the hypersurfaces are spheres or hyperquadrics,
and hence we mention some of the issues in this situation.

Given the number of positive and negative eigenvalues (signature pair)
of the source and target hyperquadrics (and hence their dimensions),
what can we say about the CR mappings between them? For example, if the mappings are assumed or known to be rational, can we give a sharp
upper bound for the degree? What rigidity results
hold, and how are they related to the signature pairs?
If the source manifold is the sphere, and the mappings
are assumed to be invariant under a finite subgroup of the unitary group,
then how do the group and its unitary representation influence the complexity? How are these ideas connected with number theory? How are these ideas connected with the differential geometry and topology of the CR manifolds?

The main topic of the workshop will thus be a part of
CR Geometry. More specifically the workshop aims to unify and clarify developing notions of complexity for CR mappings and to apply them
to other problems, both in CR Geometry and in other areas of mathematics.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.