# Andy Sanders

**Ph.D Student**

*Thesis Advisor:* Bill Goldman

Mathematics Program

University of Maryland at College
Park

** **

**Current (and future) Research**

I am primarily interested in Geometry, Topology (<5 dimensions) and Analysis. I have began research on understanding the refined picture of
Minimal Surfaces in Quasi-Fuchsian 3-manifolds (and their geometric limits) and connections with Teichmuller theory. As a graduate student,
I have been interested in various moduli spaces (Higgs Bundles, Yang-Mills connections, Teichmuller space).

** Contact Info: **
Office: 4106
Mathematics Building

University of Maryland

College Park, MD 20742-4015

* Email: * andysan (at) math.umd.edu

**Papers**

** Domains of Discontinuity of almost-Fuchsian
groups**, Preprint

In this paper we prove that the domain of discontinuity of an almost-Fuchsian group has a much
more restricted structure than that of a general quasi-Fuchsian group. Using this result, we show
that there are no singly or doubly degenerate geometric limits of almost-Fuchsian groups.

** A complete proof of the Dehn-Nielsen-Baer
Theorem**

This is an expanded proof of the Dehn-Nielsen-Baer theorem which was expanded from
the proof presented in the book "A Primer on Mapping Class groups" by
Benson Farb and Dan Margalit. This was jointly written up with Jeff
Frazier a few years ago. There is nothing original, but it might
be a useful resource for someone learning this theorem for the first time.

## Current Teaching

I am supported by the Ann G. Wylie graduate school dissertation fellowship for the Fall of 2012.

## Past Activites

** Past Teaching **

** Past Courses**