Nic Koban Associate Professor of Mathematics Office: Brinkman 105 Phone: (207) 778-7117 Email: nicholas.koban@maine.edu

TEACHING

In the Spring of 2012, I will be teaching:

• Math 104 - Mathematical Content for Elementary School Teachers II
• Math 251 - Linear Algebra

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 120 - Introductory Statistics (Fall 07 and 10, 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 08-11)
• Math 241 - Calculus III (Fall 09 and 10)
• 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)

RESEARCH

My field of interest is topology. I am especially interested in geometric group theory. My research so far has been focused on the Bieri-Neumann-Strebel-Renz geometric invariants Σⁿ of a group. My thesis develops an invariant Ωⁿ analogous to Σⁿ and investigates the relationship between the two. Recently, I have become interested in the relationship between Ωⁿ and the property R_∞ of a group. I have also focused much of my research in computing Ωⁿ 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. 1975-1993.

• N. Koban, The Geometric Invariants Ωⁿ of a Product of Groups, Geometriae Dedicata, Volume 124 (Number 1), February 2007, pp. 133-141.
  The original publication is available at www.springerlink.com

• N. Koban and P. Wong, A Relationship Between Twisted Conjugacy Classes and the Geometric Invariants Ωⁿ, Geometriae Dedicata, Volume 151 (Number 1), 2011, pp. 233-243.
  The original publication is available at www.springerlink.com

UNDERGRADUATE RESEARCH PROJECTS

I have supervised the following undergraduate research projects:

• During the 2007-2008 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 2008-2009 academic year, Dan Allen studied the braid groups, B_n, on n strands, and he computed Σ¹(B₃). 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 2008-2009 academic year for this research. His paper on this work was published in 2008-2009 Apropos. Here is a copy of his paper The Σ¹-Invariants of B₃.

• During the 2009-2010 academic year, Dan Allen studied the so-called lamplighter groups, L_m, and he computed Σⁿ(L_m). He presented his results 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 Rose-Hulman Institute of Technology Undergraduate Math Journal. Here is a link to the paper www.rose-hulman.edu/mathjournal/v11n1.php.

• During the 2010-2011 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.

EDUCATION AND EMPLOYMENT

Education

• B.S. in Mathematics from Bloomsburg University in 1997.
• Ph.D. in Mathematics from Binghamton University in 2004.

Employment

• Assistant Professor of Mathematics at Western Carolina University from fall 2004 until spring 2006.
• Assistant Professor of Mathematics at the University of Maine Farmington from fall 2006 until fall 2011.
• Associate Professor of Mathematics at the University of Maine Farmington since fall 2011.