Doing Anything You Want With Combinatorics

Dr. Jennifer Elder
Assistant Professor of Mathematics
Missouri Western State University

When Mathematical Reviews first launched as a journal in 1940, combinatorics was not listed as a research area. The Seven Bridges of Königsberg was solved in 1736, so this absence is not due to later development of the field. Combinatorics has simply been hard to define on its own, given that it is used as a tool in so many different areas of mathematics.

This talk will take the opposite point of view. We will center our focus on several research problems motivated from a combinatorial standpoint, and the connections to other fields of research. These connections can be simple, such as bridging different subareas of combinatorics: a study of a specific set of words uncovering unexpected properties of intervals in a lattice. Or the connections can be more odd, connecting widely different areas of mathematics: a study of braid diagrams on k strands as a dynamical algebraic system.