Meeting of Minds Conference (Thurs 6 June 2013): speaker abstract
Rearrangements, Degree Theory and Counting Games
Anthony Masters (Department of Mathematics, University of Bath)
Two real-valued functions are called rearrangements if the measures of pre-images of Borel sets are equal for all Borel sets. The study of rearrangements
arises naturally in fluid flow problems, as bodies of fluid retain their volume but are rearranged over time.
My research focuses upon boundary value problems involving rearrangements, seeking to apply degree theory in order to discover the multiplicity of the
solutions. Degree theory allows the assignment of whole numbers to fixed points of compact maps from the weak closure of a set of rearrangements to
itself. This assignment turns the question of how many fixed points the maximiser function has into a simple counting game. This counting game will be the
main concern of this talk.
Meeting of Minds conference