Dana Ernst, PhD
My primary research interests are in the interplay between combinatorics and algebraic structures. More specifically, I study the combinatorics of Coxeter groups and their associated Hecke algebra, Kazhdan-Lusztig theory, generalized Temperley-Lieb algebras, diagram algebras, and heaps of pieces. By employing combinatorial tools such as diagram algebras and heaps of pieces, one can gain insight into algebraic structures associated to Coxeter groups, and, conversely, the corresponding structure theory can often lead to surprising combinatorial results. The combinatorial nature of my research naturally lends itself to collaborations with advanced undergraduate students, and my goal is to incorporate undergraduates in my research as much as possible.
In addition to traditional mathematics research, I am also passionate about mathematics education. In particular, I am interested in inquiry-based learning (IBL) and the Moore method for teaching mathematics. I am currently the Special Projects Coordinator for the Academy of Inquiry-Based Learning and a mentor for several new IBL practitioners. Moreover, I actively give talks and organize workshops on the benefits of IBL as well as the nuts and bolts of how to implement it in the mathematics classroom.