Dr. Sarah A. Rundell Affiliation: Faculty Title: Associate Professor Office: Olin 203 Email: rundells@denison.edu Phone: 740-587-6600 Fax: 740-587-5749 Ph.D. in Mathematics from University of Michigan, 2007 A.B. in Mathematics from Bryn Mawr College, 2002 See full resume [pdf]

Research

My research is in algebraic and topological combinatorics. Recently, I have been particularly interested in coloring complexes. Given a simple graph with n vertices, the coloring complex associated to the graph has as its r-faces the set of all ordered partitions (B_1,...,B_{r+2}) where at least one B_i contains an edge of the graph. In my Ph.D. dissertation, I studied the cyclic coloring complex of an arbitrary simple graph and computed the dimensions of its homology groups.

Research Papers

Flapan, E., S. Rundell, and M. Wyse. "Asymmetric 2-colorings of planar graphs in S³ and S²." (Submitted to Mathematical Proceedings of the Cambridge Philosophical Society.)

Rundell, S. "The Coloring Complex and Cyclic Coloring Complex of a Complete k-uniform Hypergraph." Journal of Combinatorial Theory, Series A. 119.no.5 (2012): 1095-1109.

Long, J., and S. Rundell. "The Hodge Structure of the Coloring Complex of a Hypergraph." Discrete Math. 311.no.20 (2011): 2164-2173.

The Homology of the Cyclic Coloring Complex [pdf]
submitted, J. Combinatorial Theory, Series A.

Teaching

I love teaching any math course. During my time at Denison, I have taught Essentials of Calculus, Calculus II, Combinatorics, Abstract Algebra II, and Introduction to Proofs. I also taught a first year studies course entitled "Mathematical Perspective Drawing".