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 Piazza dei Cavalieri, 7 56126 Pisa E-mail: valeria.giuliani@sns.it E-mail: classi@sns.it -- Hai ricevuto questo messaggio perché sei iscritto al gruppo "Matematici.Esterni.SNS" di Google Gruppi. Per annullare l'iscrizione a questo gruppo e non ricevere più le sue email, invia un'email a matematici.esterni.sns+unsubscribe@sns.it. Per visualizzare questa discussione sul Web, visita https://groups.google.com/a/sns.it/d/msgid/matematici.esterni.sns/CAGKKDBkWp.... _______________________________________________ Settimanale mailing list Settimanale@fields.dm.unipi.it https://fields.dm.unipi.it/listinfo/settimanale