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Research Activities
In keeping with its goal to provide a platform for multifarious research in Mathematics, the Foundation has undertaken the following research activities:
Enumeration of Types of Finite Groups and Associated Topics: This is a research project in pure mathematics. A basic question one can ask about finite groups is this: how many groups are there up to an isomorphism of a given order? We have been looking at questions relating to the enumeration of finite soluble groups with abelian Sylow subgroups. It has led to interesting work and collaboration with several mathematicians. A monograph (written jointly by Geetha Venkataraman, Peter Neumann and Simon Blackburn) is to be published shortly by the Oxford University Press.
Linear Mappings Associated with Banach Spaces of Functions: This research project deals with the investigation of properties of certain bounded linear transformations on a class of Banach and Hilbert spaces of analytical functions. Amongst the spaces that are looked at are the BMOA and VMOA, Hardy spaces, De Branges spaces and other related spaces. Several related research papers have taken off from this project in some very important areas. It has led to a series of collaborative efforts between Mathematicians at the Foundation and in the USA.