CR Geometry and Hermitian Forms
Time and place
1 PM on Tuesday, March 9th, 2010; NAC 6113
Prof. Jiri Lebl (University of Illinois, Urbana-Champaign)
Abstract
CR geometry is the study of the Cauchy-Riemann equations restricted to a real manifold in complex space. I will outline a connection between CR geometry and Hermitian forms. In particular, I will talk about CR mappings of spheres in different dimensions, and I will give a complete classification of all such rational maps of degree 2. I will also mention some results on the case of diagonal Hermitian forms as such results are sometimes sufficient for the study of the general problem. Lots of difficult and fascinating combinatorics arises even in the diagonal case.