Mathematics Colloquium

Wednesday, 31 Jan. 4 pm

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Venue: Ramanujan Hall

Host: Prachi Mahajan

Speaker: Debraj Chakrabarti

Affiliation: Central Michigan University, Mt. Pleasant, MI

Title: Convexity conditions and complex analysis

Abstract: The global geometric properties of a space affect the properties of functions that can be defined on it: for example, on a connected topological space a locally constant function is constant. In complex analysis,  complex convexity properties such as pseudo convexity play a crucial role in the construction and properties of holomorphic functions and other analytic objects. These conditions become very important in several complex variables since in domains in the plane the required convexity conditions are automatically satisfied. 

After introducing classical complex convexity conditions, we discuss partial convexity conditions, which lead to the vanishing of Dolbeault cohomology in specified degrees. At the end, we will introduce some new geometric conditions that allow us to prove the vanishing of Dolbeault cohomology in domains in complex manifolds.

This is ongoing joint work with Phil Harrington and Andy Raich of the University of Arkansas.

We will try to make the talk accessible to a wide audience.