[CvGmt News] Avviso seminario di matematica, prof. Cheng Jih-Hsin (10.05.16)

[Michele Verde]

SEMINARIO DI MATEMATICA



*martedì 10 maggio 2016*

ore 15:00



*Scuola Normale Superiore*

Pisa

Aula Tonelli



*Cheng Jih-Hsin*

*Academia Sinica*



Terrà un seminario dal titolo:



*“**A local index theorem for CR manifolds with $S^1$ action**”*





*Abstract:*

*Among those transversally elliptic operators initiated by Atiyah and
Singer, Kohn's $\Box_b$ operator on CR manifolds with $S^1$ action is a
natural one of geometric significance for complex analysts. Our main result
computes a local index density, in terms of \emph{tangential}
characteristic forms, on such manifolds including \emph{Sasakian manifolds}
of interest in String Theory. As applications of our CR index theorem we
can prove a CR version of Grauert-Riemenschneider criterion, and produce
many CR functions on a weakly pseudoconvex CR manifold with transversal
$S^1$ action and many CR sections on some class of CR manifolds, answering
some long-standing questions raised by Kohn and Henkin respectively.
Moreover in some cases, we can reinterpret Kawasaki's
Hirzebruch-Riemann-Roch formula for a complex orbifold with an orbifold
holomorphic line bundle as an index theorem obtained by an integral over a
smooth CR manifold which is essentially the circle bundle of this line
bundle. This is joint work with Chin-Yu Hsiao and I-Hsun Tsai*



Tutti gli interessati sono invitati a partecipare.




Classe di Scienze


Matematiche e Naturali

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