Fusheng Deng

On biholomorphisms between bounded quasi-Reinhardt domains

In this paper, we define what is called a quasi-Reinhardt domain and study biholomorphisms between such domains. We show that all biholomorphisms between two bounded quasi-Reinhardt domains fixing the origin are polynomial mappings, and we give a uniform upper bound for the degree of such polynomial mappings. In particular, we generalize the classical Cartan’s linearity theorem for circular domains to quasi-Reinhardt domains.

On fermionic representation of the framed topological vertex

A bstractThe Gromov-Witten invariants of ℂ3

Group Actions in Several Complex Variables: A Survey

{\mathbb{C}}^3

PROPERTIES OF SQUEEZING FUNCTIONS AND GLOBAL TRANSFORMATIONS OF BOUNDED DOMAINS

with branes is encoded in the topological vertex which has a very complicated combinatorial expression. A simple formula for the topological vertex was proposed by Aganagic et al. in the fermionic picture. We will propose a similar formula for the framed topological vertex and prove it in the case when there are one or two branes.

Positivity of direct images of positively curved volume forms

A bstractWe will establish the fermionic gluing principle of the topological vertex, that is, provided the framed ADKMV conjecture, the generating functions of the Gromov-Witten invariants of all toric Calabi-Yau threefolds are Bogoliubov transforms of the vacuum.

Positivity of character subbundles and minimum principle for noncompact group actions

We give a survey on some recent developments about group actions in several complex variables, including rigidity of the automorphism groups of the invariant domains in Stein homogenous spaces under complex reductive groups, and extension and rigidity of the proper holomorphic mappings of the domains in \(\mathbb C^n\) with symmetries.