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).
University of Maryland
College Park, MD 20742-4015
Email: andysan (at) math.umd.edu
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.