Matthew Horak

Associate Professor
Mathematics Statistics and Computer Science

Office: 307 Jarvis Hall - Science Wing
Phone: 715/232-2393
Email: horakm@uwstout.edu


Research

Overview:

My speciality is geometric group theory, in which the main idea is to view groups as geometric objects with the hope of using geometric reasoning to discover algebraic facts.  One way to view a finitely generated group G geometrically is to construct its Cayley graph with respect to a finite generating set S.  This graph has one vertex for every group element and an edge connecting elements g and h if g^{-1}h or h^{-1}g belongs to S.

My recent projects involve Thompson's groups F, T and V.  Working with Melanie Stein and Jennifer Taback, I have found a way to determine length in F with respect to the standard generating sets.  This allows us to study various properties of F with respect to these generating sets, such as almost-convexity and the dead end depth.  For more on these projects, follow the "Research" and "Publications" links to the right.

I also led a research group at the BYU REU during the summer of 2011.  My group expanded the family of generating sets of F for which we can calculate word length and sharpened the known bounds on the dead end depth of F.  This research lead to two student-coauthored publications now under review.

Summer 2012 REU:

This summer, I will be leading another NSF-sponsored REU group at UW-Stout.  My group will again study geometric group theory.  A likely topic is further study of Thompson's groups F and T, possibly with the aim of determining word length in T.  Another possible topic is to analyze the behavior of infinite quasi-geodesic rays in F or other interesting finitely generated groups.

Other groups at the UW-Stout mathematics REU will study complex analysis and algebraic geometry.  For more information or to apply for the REU visit my REU information page.



Teaching:

Fall Courses 2011

  • Math 157-001, Calculus and Analytic Geometry II
  • Math 275-001, Linear Algebra
  • Math 270-001, Discrete Mathematics

The course web pages are available through Learn@UW-Stout.

Office Hours (Fall 2011)

Conducted in JHSW 307 unless otherwise noted:

  • Monday 1:30 - 3:30
  • Tuesday 10:10- 12:10
  • Wednesday 1:20 - 3:30
  • Friday 1:30 - 3:30

Also by appointment and whenever I am in.