Welcome! My name is Dana C. Ernst and I am an assistant professor in the Department of Mathematics and Statistics at Northern Arizona University in Flagstaff, AZ. This site is part of the Booles’ Rings network of academic home pages/blogs. Unless indicated otherwise, all of the work contained in this site is licensed under a Creative Commons Attribution-Share Alike 4.0 United States License.
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 algebras, 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. More recently, my research has expanded into combinatorial game theory (joint with Nandor Sieben and Bret Benesh). In particular, our research has focused on avoidance and achievement games involving finite groups. The combinatorial nature of my research naturally lends itself to collaborations with undergraduate students, and my goal is to incorporate undergraduates in my research as much as possible.
My interests also include the scholarship of teaching and learning (SoTL) with a focus on inquiry-based learning (IBL) as an approach to teaching/exploring mathematics. I am currently a 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 this approach in the mathematics classroom.
Unless stated otherwise, content on this site that is authored by Dana C. Ernst is licensed under a Creative Commons Attribution-Share Alike 4.0 International License.
The views expressed here are my own and are not necessarily shared by Northern Arizona University.