Sarah A. Rundell
Sarah Rundell joined the Denison faculty in 2007. She grew up near Boston, Massachusetts and did her undergraduate work at Bryn Mawr College, where she received an A.B. in Mathematics. She received her Ph.D. from the University of Michigan under the direction of Phil Hanlon.
During her time at Denison, she taught in the Mathematics Department for 15 years, was a Process Advisor for Academic Integrity for four years, and was the Academic First-Year and Sophomore Dean. Dean Sarah is currently the Sophomore Dean and Director of Advising, and she is the Posse Mentor for Posse Boston 15. As Sophomore Dean and Director of Advising, Dean Sarah strives to build strong relationships with students to help support them as whole students, and she works to create community within the Sophomore class through small group activities. The Sophomore Year is one of much growth and discernment, and Dean Sarah also works to help Sophomores connect to resources on campus that have special programming geared towards Sophomores, all of which is part of Denison’s new Sophomore Experience.
Research
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.
Works
Selected publications:
- 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
Other
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.