SCHEDULE (Spring 2014)


MONDAY 
TUESDAY 
WEDNESDAY 
THURSDAY 
FRIDAY 
8:008:30 
Math 104 
Unavailable 
Math 104 
Research Time (Unavailable) 
Math 104 
8:309:05 
9:159:45 
Math 104 

Math 104 
Math 104 
9:4510:20 
Meet with Research Asst 
10:3011:00 
Math 304 
Math 304 
Math 304 
11:0011:35 

11:3512:00 
Meetings/ Gym 

Gym 
Meetings/ Gym 
12:0012:30 
Office Hour 
12:301:00 
1:001:30 




1:302:00 
Office Hour 



2:002:30 
Office Hour 

Office Hour 
2:303:00 


3:003:30 
Unavailable 

Unavailable 

3:304:00 


TEACHING
In the spring of 2014, I will be teaching the following courses:
Past Teaching at the University of Maine Farmington
I have taught the following courses at UMF:
 Math 100  Introduction to Mathematics (Fall 08)
 Math 103  Mathematical Content for Elementary School Teachers I (Fall 08 and 11)
 Math 104  Mathematical Content for Elementary School Teachers II (Spring 12)
 Math 120  Introductory Statistics (Fall 07, 10, 12 and 13, Spring 08, 09, 10 and 11, Summer 11)
 Math 132  Precalculus (Fall 06, Spring 07, 08 and 11, Summer 07 and 08)
 Math 141  Calculus I (Fall 06, 07, and 09 and Summer 09)
 Math 142  Calculus II (Summer 07 and 08)
 Math 151  Foundations of Abstract Mathematics (Spring 07, Fall 0811 and 13)
 Math 241  Calculus III (Fall 09, 10, and 12)
 Math 251  Linear Algebra (Spring 12)
 Math 304  College Geometry (Spring 07 and 08)
 Math 352  Abstract Algebra (Spring 09 and 11)
 Math 403  Numerical Analysis/Differential Equations (Fall 07)
 Math 477  Real Analysis (Spring 10 and Fall 12)
 Math 477  Geometric Group Theory (Fall 13)
RESEARCH
My field of interest is topology. I am especially interested in geometric
group theory. My research so far has been focused on the
BieriNeumannStrebelRenz geometric invariants Σ^{n}
of a group. My dissertation develops
an invariant Ω^{n} analogous to Σ^{n} and
investigates the
relationship between the two. Recently, I have become interested in the relationship between Ω^{n} and the property R_{∞} of a group. I have also focused much of my research in computing Ω^{n} for certain products of groups.
Research Papers
 N. Koban, Controlled Topology Invariants of Translation Actions, Topology and it's Applications, Volume 153 (Issue 12), 2006, pp. 19751993.
 N. Koban, The Geometric Invariants Ω^{n} of a Product of Groups, Geometriae Dedicata, Volume 124 (Number 1), February 2007, pp. 133141.
The original publication is available at www.springerlink.com
 N. Koban and P. Wong, A Relationship Between Twisted Conjugacy Classes and the Geometric Invariants Ω^{n}, Geometriae Dedicata, Volume 151 (Number 1), 2011, pp. 233243.
The original publication is available at www.springerlink.com
 N. Koban, J. McCammond, and J. Meier, The BNSInvariant of the Pure Braid Groups, to appear in Groups, Geometry, and Dynamics.
 N. Koban and A. Piggott, The BieriNeumannStrebel Invariant of the Pure Symmetric Automorphisms of a Rightangled Artin Group, to appear in the Illinois Journal of Mathematics.
UNDERGRADUATE RESEARCH PROJECTS
I have supervised the following undergraduate research projects:
 During the 20072008 academic year, Sam Valentine researched the origins of the Pythagorean Theorem in Chinese history. Sam conducted a large portion of his research while studying in China during the spring 2008 semester. He presented his findings (via skype from China) at the 2008 Michael D. Wilson Symposium day. Sam was named a Wilson Scholar for this research during the fall semester of 2007.
 During the 20082009 academic year, Dan Allen studied the braid groups, B_{n}, on n strands, and he computed Σ^{1}(B_{3}). He also studied the general structure of the Cayley graphs of the braid groups on n strands. He presented his results at a UMF math hour talk in April of 2009 and also at the 2009 Michael D. Wilson Symposium day. Dan was named the Wilson Fellow for the 20082009 academic year for this research. His paper on this work was published in 20082009 Apropos. Here is a copy of his paper The Σ^{1}Invariants of B_{3}.
 During the 20092010 academic year, Dan Allen studied the socalled lamplighter groups, L_{m}, and he computed Σ^{n}(L_{m}). He presented his results at a UMF math hour talk in April of 2010 and also at the 2010 Michael D. Wilson Symposium day. Dan was named a Wilson Scholar for this research during the fall semester of 2009. His paper on this work was published in the RoseHulman Institute of Technology Undergraduate Math Journal. Here is a link to the paper www.rosehulman.edu/mathjournal/v11n1.php.
 During the 20102011 academic year, Garret LaForge studied free products with amalgamation. He studied the real vector space of characters of these products (in terms of the character spaces of the individual groups) and the Cayley graphs of amalgamated products. He presented his results at a UMF math hour talk in April of 2011 and also at the 2011 Michael D. Wilson Symposium day. Garret was named a Wilson Scholar for this research during the fall semester of 2010.
 During the 20112012 academic year, Tom Kilcoyne computed Σ^{1}(G) where G is the semidirect product of a free abelian group acting on a free group by certain pure symmetric automorphisms. He presented his results at a UMF math hour talk in April of 2012 and also at the 2012 Michael D. Wilson Symposium day. Tom was named a Wilson Fellow for the 20112012 academic year for his research. His work will be continued by Adam Black during the 20122013 academic year.
 During the 20122013 academic year, Adam Black worked on two different projects. He worked on the Σ^{1} invariant for groups with finite complete geodesic rewriting systems. He presented his results at the 2013 Michael D. Wilson Symposium day. Adam was named a Wilson Scholar for the fall semester of 2012 for this research. He also continued the work of Tom Kilcoyne by computing Σ^{1}(G) where G is the semidirect product of a free abelian group acting on a free group by certain pure symmetric automorphisms.
EDUCATION AND EMPLOYMENT
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