Matthew Horak
Assistant Professor
University of Wisconsin-Stout

&bull Contact Information:

Department of Mathematics Statistics and Computer Science
University of Wisconsin-Stout
Harvey Hall 237
Menomonie, WI 54751

Office: Harvey 237E
Phone: (715) 232-2301
Fax: (715) 232-2573
horakm@uwstout.edu

&bull Teaching, Summer 2009:

Statistics 130-003

• Online, May 26 - July 2, 2009

Data Sets

CrunchIt! Intro

CrunchIt! 2.0 Summary and Graphing

Excel 2-Variable Problems 5

&bull Teaching, Spring 2009:

Math 154-001, Calculus II

• MTWTh, 11:15 - 12:20;
  

Math 370-001, Modern Algebra II

• MWF, 10:10 - 11:05;
  

Stat 130-005,006, Elementary Statistics

• MTWTh, 1:25 - 2:20;
  

The course webpages are available through Learn@uw-stout.

Office Hours (Spring 2009), in Harvey 237E unless otherwise noted:

• Monday 9:00 - 10:00
• Tuesday 9:00 - 11:00, 2:30 - 3:30
• Wednesday 9:00 - 10:00, 12:00 - 1:00
• Thursday 9:00 - 10:00
• Friday 9:00 - 10:00
• By appointment and whenever I am in.

&bull Research:

Fall 2008 Eastern Section AMS Meeting

With Melanie Stein and Jennifer Taback, I am organizing a Special Session on Geometric Group Theory and Topology at the 2008 Fall Eastern Section Meeting of the AMS on October 11 - 12, 2008 in Middletown, CT. More information on this session is available here.

Research Interests:

Graph Theory

For the 2008 - 2009 academic year, I received a mini-grant from the Center for Undergraduate Research in Mathematics (CURM) to support work with four students, Eric LaRose, Jessica Moore, Mic Rooney and Hannah Rosenthal. We studied a property of metric spaces called "roundness" in the context of graphs. We simply investigated the question of what possible values can occur as the roundness of a finite graph. Two of the students, Eric and Hannah wrote a Java program that takes the adjacency matrix for a graph with 10 or fewer vertices and estimates its roundness (with "3" meaning "infinity"). This version of the program is good for general experimentation, but they also modified it to read in adjacency matrices from a file and then managed to compute the roundness of all of the connected graphs with 6, 7, 8, or 9 vertices. Jessica and Mic took a more theoretical approach, investigating the roundness of various infinite families of graphs. Among other things, Mic looked at cyclic graphs and Jessica looked at triangulated cyclic graphs. Both managed to find (with proof) the roundness of the graphs in their classes.

Thompson's Group

With Melanie Stein, of Trinity College and Jennifer Taback of Bowdoin College I have become interested in studying the word metric and convexity properties of Thompson's group F.

Mapping class groups and Out(Fn)

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 understood much better. This involves studying actions of these groups on complexes of graphs such as Outer space and ribbon graph complexes.

Ordered groups and order trees

With Melanie Stein, 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 is a first step in studying partially ordered groups by way of their actions on various geometric objects.

Knot theory

During the summer of 2005, 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 she found at the Spuyten Duyvil Undergraduate Mathematics Conference at Manhattan College.

A more detailed summary of my current research interests is available in my statement of research interests.

&bull Publications, Preprints and Conferences

Research Papers:

1. Horak, M., Stein, M., and Taback, J., Convexity properties of Thompson`s group F
   arXiv:arXiv:0801.1862.
   
   
2. Horak, M., Stein, M., and Taback, J., Computing word length in alternate presentations of Thompson`s group F
   arXiv:arXiv:0706.3218.
   
   
3. Horak, M., and Stein, M. Partially ordered groups which act on oriented order trees, Rocky Mountain Journal of Mathematics, to appear.
   arXiv:math.GR/0503407.
   
   
4. Horak, M., Mapping class subgroups of Out(Fn), Pacific Journal of Mathematics, 227 (2007), No. 1, 65-94.
   arXiv:math.GT/0310328
   
   
5. Becker, J., Horak, M. and VanWyk, L. Presentations of subgroups of Artin groups, Missouri J. Math. Sci. 10 (1998), No. 1, 3-14.
   MJMS
   
   

Expository and Teaching Papers:

1. Horak, M., Disentangling topological puzzles by using knot theory, Mathematics Magazine 79:4 (2006), 368 - 375.
   PDF
   
   
2. Becker, J., Ghenciu, P., Horak, M., Schroeder, H., A College Lesson Study in Calculus, Preliminary Report, International Journal of Mathematical Education in Science and Technology, Volume 39 Issue 4, June 2008, 491-503. PDF; Author Posting. (c) Taylor and Francis, 2008.

   This is the author's version of the work. It is posted here by permission of Taylor and Francis for personal use, not for redistribution. The definitive version was published in International Journal of Mathematical Education in Science and Technology, Volume 39 Issue 4, June 2008. doi:10.1080/00207390701867463, (http://dx.doi.org/10.1080/00207390701867463)

Conference Talks:

1. Horak, M., Stein, M., Taback, J. Length and convexity in Thompson`s Group F, Spring 2008 Southeastern Section Meeting of the AMS.
   
   
2. Horak, M., Stein, M., Taback, J. Length in Thompson`s Group F, Fall 2006 Western Section Meeting of the AMS.
   
   
3. Horak, M., Steim, M. An order-theoretic characterization of groups admitting actions on oriented order trees, Fall 2005 Eastern Section of the AMS.