Matthew Horak Dorwart Assistant Professor
Trinity College
Matthew Horak
Department of Mathematics
Trinity College
300 Summit Street
Hartford, CT 06106-3100
Office: MCEC 227
Phone: (860) 297-5343
Fax: (860) 987-6239
matthew.horak@trincoll.edu
Math 107, Elementary Statistics
This is the field of my dissertation research at Cornell University under Karen Vogtmann. The idea is to try to understand the homology of Out(Fn) in terms of mapping class groups of surfaces, because their homology is much better understood. This involves acting these groups on complexes of graphs such as Outer space and ribbon graph complexes.
With Melanie Stein, at Trinity College, I've become involved in an effort to study partially ordered groups by way of their actions on oriented order trees. We've found a characterization of the left-invariant partial orders on a group that can arise from a action of that group on an order tree. This will hopefully lead the way to studying partially ordered groups by way of their actions on various geometric objects.
Over the summer, I worked with Alexis Morley-Lyons on a research project in knot theory. We focused on the so-called "rational tangles." Our goal was to find an relatively easy way to determine whether or not a given tangle diagram represents a rational tangle. Alexis presented the results of these efforts at the Trinity College Summer Research Symposium and will shortly be posting the solution on the mathematics department webpage.
A more detailed summary of my current research interests is available in my statement of research interests.