Title: Sobolev Steepest Descent for Differential Equations

Abstract:  Solving differential equations using steepest descent methods based on the Euclidean norm has long been established as ineffective, although pre-conditioning techniques  may alleviate this problem to some extent. However, steepest descent in spaces with a better choice of norm can be quite efficient.    Beginning with an example accessible to undergraduates, we will outline Sobolev descent on a few elementary examples and demonstrate at least one interesting open problem in the area.  This talk should be accessible to undergraduates, graduate students and faculty not necessarily experts in numerical differential equations.
Title: Finite group actions, orbifolds, and equivalence of group actions

Abstract: A handlebody orbifold consists of finitely many quotients of the 3-ball by spherical groups (Zn, Dn, A4, S4, and A5) connected by 1-handle orbifolds respecting singular axes and their orders, and such that topologically the outcome is an orientable handlebody. We will first examine the handlebody of genus two, V2, and the handlebody orbifolds V2/G, where G is a finite group. We will then discuss equivalence of group actions and see that, up to equivalence, there are 13 actions on V2. This will lead into my work, where we consider cyclic p-squared actions, where p is prime, on a handlebody of genus g.