Differential topology of almost complex manifolds and its applications

Lead Research Organisation: University of Warwick
Department Name: Mathematics

Abstract

Thomas Holt will study almost complex manifolds guided by the philosophy that a statement for smooth maps between smooth manifolds in terms of Thom's transversality should also have its counterpart in pseudoholomorphic setting without requiring the transversality or genericity, but using the notion of pseudoholomorphic subvarieties, in particular when such a statement is available in complex analytic setting. The topics would contain the intersection of almost complex manifolds, pseudoholomorphic maps and rational maps between almost complex manifolds, and birational invariants of almost complex manifolds like Kodaira dimensions and plurigenera. The research aims to set up the differential topology aspect of almost complex geometry and build new connections between different mathematical disciplines through almost complex geometry. The main beneficiaries of the proposed research will be research mathematicians working in differential geometry, symplectic geometry and complex geometry.

Publications

10 25 50

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/R513374/1 01/10/2018 30/09/2023
2105841 Studentship EP/R513374/1 01/10/2018 31/03/2022 Thomas Charles Holt