Speaker:

Yat Sun Poon, Professor of Mathematics,

Department of Mathematics,

University of California-Riverside

Title: Generalized Deformation of Abelian Complex Structures on Nilmanifolds

Abstract: Nilmanifolds are co-compact quotients of nilpotent Lie groups. Some of them admit an invariant complex structure such that the algebra of complex (1,0)-vectors is an abelian Lie algebra. For this type of complex structures, we demonstrate how one may compute its deformation and provide a complete description on integrability when the complex-dimension of the nilmanifolds is equal to three.