## September 16, Ted Mahavier, Lamar University

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- Category: 2016-2017

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.

## September 23, Jesse Prince-Lubawy, University of North Alabama

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- Category: 2016-2017

Abstract: A handlebody orbifold consists of finitely many quotients of the 3-ball by spherical groups (

**,**

*Z*_{n}**,**

*D*_{n}**,**

*A*_{4}**, and**

*S*_{4}**) 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,**

*A*_{5}*V*, and the handlebody orbifolds

_{2}*V*/

_{2}*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

*V*. This will lead into my work, where we consider cyclic

_{2}*p*-squared actions, where

*p*is prime, on a handlebody of genus

*g*.