[CvGmt News] [Notiziario] [Settimanale] avviso Seminario prof. Jih-Hsin Cheng (14.10.2019)

[Valeria Giuliani]

SEMINARIO DI MATEMATICA



*Lunedì 14 ottobre 2019*

ore 14:00



*Scuola Normale Superiore*

Pisa

Aula Mancini



*Jih-Hsin **Cheng*
*(Priceton University**)*



Terrà un seminario dal titolo:
“Heat kernel and local index theorem for open complex manifolds
with $\mathbb{C}^{\ast }$ action”



*Abstract:*



For a complex manifold with $\mathbb{C}^{\ast }$ action, we define the
$m$-th $\mathbb{C}^{\ast }$ Fourier-Dolbeault cohomology group and consider
the $m$-index. By applying the method of \textit{transversal} heat kernel
asymptotics, we obtain a local index formula for the $m$-index. We can
reinterpret Kawasaki's Hirzebruch-Riemann-Roch formula for a compact
complex orbifold with an orbifold holomorphic line bundle by our single
integral over a (smooth) complex manifold. We generalize $\mathbb{C}^{\ast
}$ action to complex semisimple Lie group $G$ action on a compact or
noncompact complex manifold. Among others, we study the nonextendability of
open group action and the space of all $G$ invariant holomorphic
$p$-forms. Finally,
in the case of two compatible holomorphic $\mathbb{C}^{\ast }$ actions, a
mirror-symmetry type isomorphism is found between two linear spaces of
holomorphic forms, and the Euler characteristic associated with these
spaces can be computed by our $\mathbb{C}^{\ast }$ local index formula on
the total space. This is joint work with Chin-Yu Hsiao and I-Hsun Tsai.



Tutti gli interessati sono invitati a partecipare.



Classe di Scienze
Valeria Giuliani
Scuola Normale Superiore
Servizio alla Didattica e Allievi
tel. 050 509260
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56126 Pisa
E-mail: valeria.giuliani at sns.it
E-mail: classi at sns.it

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