Generalized Separation of Collections of Sets

Project Title:

Generalized Separation of Collections of Sets

Supervisor:

A/Prof Alexander Kruger

Contact person and email address:

Alexander Kruger a.kruger@federation.edu.au

A brief description of the project:

The core arguments used in various proofs of the extremal principle and its extensions as well as in primal and dual characterisations of approximate stationarity and transversality of collections of sets to be exposed, analysed and refined, leading to a unifying theory, encompassing all existing approaches to obtaining ‘extremal' statements   . For that, quantitative relationships between the parameters involved in the respective definitions and statements are to be examined and clarified.

The topic is broad, and the actual scope of the project can be negotiated and adjusted depending on the experience and research interests of the applicant. Several PhD projects within the above tentative topic are possible.