"My field is geometric group theory, which sits at the intersection of geometry and modern algebra. Groups are abstract objects which let us generalize operations like addition and multiplication. Geometric group theory attempts to study groups by finding metric space whose symmetries behave like a given group. Such a situation can reveal a great deal about both the algebraic structure of the group and the geometric structure of the space.
Within geometric group theory, my particular interests include the free group, its actions on trees, and its lattice of subgroups. I am also increasingly interested in the various algorithmic and statistical properties of the free group. I am also investigating the Gamma-limit groups of Sela, a fairly new class of groups with interesting geometric and residual properties which has many implications in logic and algebraic geometry over groups."
Years at Knox: 2011 to present
Ph.D., Mathematics, 2011, University of Illinois at Urbana-Champaign.
B.S., Mathematics/Computer Science, 2001, Colorado School of Mines.
Group theory, combinatorics
Research Assistantship Spring 2007, 2008, and 2009.
Finalist for Department of Mathematics TA Instructional Award AY 2008-2009 and AY 2009-2010.
Research Experiences for Graduate Students, Summer 2005.
Quantitative Residual Properties of -Limit Groups, in preparation.
Algorithmic Properties of Filling Subgroups, in preparation.
Genericity of Filling Elements, Internat. J. Algebra Comput., to appear.
"Quantifying the Residual Property of -Limit Groups." UIUC Group Theory Seminar, March 2011.
"Algorithmic and Genericity Properties of Filling Elements." UIUC Group Theory Seminar, September 2009.
"RTGWorkshop on Geometric Group Theory." University of Michigan, April 17-19, 2009.
"Examples of Groups Ohio State University." May 31-June 6, 2008.
"The Bestvina-Feighn Combination Theorem." UIUC Group Theory Seminar, September 2008.
"Polynomial-Time Word Problems, UIUC Group Theory Seminar." UIUC Group Theory Seminar, March 2007.
"Morse Theory and Finiteness Properties of Groups." UIUC Graduate Student Topology Seminar, January 2007.
Knox's Team X-Ray places second among 15 liberal arts colleges that competed in an intense regional contest involving programming teams from colleges and universities in five states.
Finals and term projects can be more than tests and papers, as Knox College faculty make engaging assignments and exams -- including design your own superhero -- to evaluate student academic achievements.
A Knox College graduate and vice president of development at the Greater Peoria Business Alliance, Jim Lynch is among the young leaders recognized by InterBusiness Issues magazine.