Analysis Seminar
Speaker: Ilya Kossovskiy (Western)
"On the stability group of a 2-nondegenerate hypersurface in $\mathbb C^3$"
Time: 14:30
Room: MC 107
Real hypersurfaces in a complex space $\mathbb C^N, N \geq 2$,
satisfying the Levi non-degeneracy condition, were very well studied
in the famous works of Poincare, Cartan, Tanaka, Chern and Moser and
in a large number of further papers. The Levi-degenerate case, which
is trivial for $N=2$ (all Levi degenerate hypersurfaces in this case
are essentially flat), turns out to be absolutely non-trivial for
$N=3$. The reason is that a hypersurface in $\mathbb C^3$ can have
Levi form of rank $1$ at a generic point, and, in this case, is
neither Levi-flat nor Levi non-degenerate. If, in addition, it
satisfies some non-degeneracy condition, guaranteeing that it can not
be reduced to a product of a hypersurface in $\mathbb C^2$ and a
complex line, the hypersurface is called 2-nondegenerate.
2-nondegenerate hypersurfaces in $\mathbb C^3$ were deeply studied in
a series of papers by Ebenfelt, Beloshapka, Zaitsev, Merker, Fels and
Kaup and many other authors, but a lot of essential questions,
concerned with their holomorphic classification and symmetry groups,
remained opened. In the present talk we demonstrate a new approach to
the study of 2-nondegenerate hypersurfaces, based on the consideration
of degenerate quadratic models. This new point of view enables us to
give a complete solution for most of the above open questions.
Mathematics Calendar 
Week of September 11, 2011
