What is mathematical finance? - by Peter Bell.
Basics of Mathematical Finance will be presented using concepts from probability. Risk measu res and option replication strategies will be introduced, which allow the introduction of fundamental theorems of asset pricing. Brief results from the author's research concerning regularity of profits under technical trading rules will be also presented.
When is an infinitesimal isometry on a Hermitian manifold holomorphic? - by Kael Dixon.
I will present this open problem in complex geometry via the example of a Hopf surface. This is (roughly) the only compact Hermitian surface that admits infinitesimal isometries which are not holomorphic, and it exhibits some interesting behaviour which is indicative of some known results in higher dimensions. This talk will not require very much knowledge of differential geometry, with most of the discussion on the more intuitive level of group actions by Lie groups.