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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
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Teaching, Fall 2008:
Math 154-001, Calculus II
Math 154-002, Calculus II
Math 370-001, Modern Algebra I
The course webpages are available through Learn@uw-stout.
Office Hours (Spring 2008), in Harvey 237E unless otherwise noted:
- Monday 10:05 - 11:05, 1:30 - 2:30 (Harvey 402 for the afternoon)
- Tuesday 10:05 - 11:05, 1:30 - 2:30 (Harvey 402 for the afternoon)
- Wednesday 10:05 - 11:05
- Thursday 10:05 - 11:05, 1:30 - 2:30
- Friday 10:05 - 11:05
- By appointment and whenever I am in.
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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:
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 much better understood. 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, 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.
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.
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Publications, Preprints and Conferences
Research Papers:
- Horak, M., Stein, M., and Taback, J., Convexity properties of Thompson`s group F
arXiv:arXiv:0801.1862.
- Horak, M., Stein, M., and Taback, J., Computing word length in alternate presentations of Thompson`s group F
arXiv:arXiv:0706.3218.
- 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.
- Horak, M., Mapping class subgroups of Out(Fn), Pacific Journal of Mathematics, 227 (2007), No. 1, 65-94.
arXiv:math.GT/0310328
- 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:
- Horak, M., Disentangling topological puzzles by using knot theory, Mathematics Magazine 79:4 (2006), 368 - 375.
PDF
- 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. 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:
Matthew Horak