We will discuss some of the local theory of rigid-analytic spaces including Tate's algebra, affinoid algebras, Washnitzer's algebra and dagger algebras. After we provide enough motivation we will discuss the results of research completed by myself and Professor Daqing Wan. The results of this research form a basis for generalizing Washnitzer's algebra.

The Sage mathematics software project (http://www.sagemath.org) aims to "Create a viable free open source alternative to Magma, Maple, Mathematica and Matlab."

This hands-on introduction to Sage will get new users solving their computational problems quickly. Emphasis will be placed on using Sage for current research and for using Sage in teaching calculus to undergraduate students.

We will use Sage on the web (http://www.sagenb.org); please bring your laptop if you have one.

The Hodge group (aka special Mumford-Tate group) of a complex abelian variety $X$ is a certain linear reductive algebraic group over the rationals that is closely related to the endomorphism ring of $X$. (For example, the Hodge group is commutative if and only if $X$ is an abelian variety of CM-type.) In this talk I discuss" lower bounds" for the center of Hodge groups of superelliptic jacobians. (This is a joint work with Jiangwei Xue.)