Sarah Rundell grew up in the Boston area, and she did her undergraduate work at Bryn Mawr College, where she earned an A.B. in Mathematics. She received her Ph.D. from the University of Michigan - Ann Arbor under the direction of Phil Hanlon, and she joined the Denison faculty in 2007. Dr. Rundell enjoys teaching a variety of math courses, including Calculus, Combinatorics, Introduction to Proofs, Linear Algebra and Differential Equations, and Operations Research. She also serves as a Process Advisor for the Academic Integrity Process at Denison.
Combinatorics is a field of mathematics that deals with the study of discrete structures. At Denison, I teach a course in enumerative combinatorics that covers different methods for counting certain discrete structures, and I am interested in directing student research projects in this field. My research interests lie in algebraic and topological combinatorics, which means that I use algebraic and topological tools to study discrete structures. Recently, I have been interested in the coloring complex and the relationships between the topology of the coloring complex and the chromatic polynomial of the underlying graph, hypergraph, or signed graph.
- Hyperoctahedral Eulerian idempotents, Hodge decompositions, and signed graph coloring complexes (with B. Braun), submitted to the Electronic Journal of Combinatorics, 2013
- Asymmetric 2-colorings of planar graphs in S^3 and S^2 (with E. Flapan and M. Wyse), submitted to the Journal of Graph Theory, 2013
- The coloring complex and cyclic coloring complex of a complete k-uniform hypergraph, Journal of Combinatorial Theory, Series A. 119. no. 5: 1095-1109, 2012
- The Hodge structure of the coloring complex of a hypergraph (with J. Long), Discrete Mathematics 311 no. 20: 2164-2173, 2011
- The homology of the cyclic coloring complex of a simple graph, Journal of Combinatorial Theory, Series A, 116, no. 3: 595-612, 2009
Selected student research projects:
- Nathaniel Kell, Investigation of Coloring Complexes in Hypergraphs, Summer 2012.
- Mary Kimberly and Beidi Qiang, A Combinatorial Interpretation of a Kostka Matrix Identity, Summer 2010.