Welcome! My name is Dana Ernst and I am an assistant professor in the Department of Mathematics and Statistics at Northern Arizona University in Flagstaff, AZ. This blog is part of the Booles’ Rings network of academic home pages/blogs.
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. See my scholarship page for more information.
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. If you are an NAU student interested in conducting research in mathematics, please come talk to me! Occasionally, there may be funding available to pay students to do research. Check out my undergraduate research page for examples of recent projects.
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.
Angie Hodge and I are coauthors for Math Ed Matters, which is a (roughly) monthly column sponsored by the Mathematical Association of America. The column explores topics and current events related to undergraduate mathematics education. Posts aim to inspire, provoke deep thought, and provide ideas for the mathematics classroom. Our interest in and engagement with IBL color the column’s content.
Besides blogging here and for Math Ed Matters, I am also an editor for Mathblogging.org, which is a site devoted to aggregating the multitude of math-related blogs and news sources across the Internet. My job as editor is to select a blog posts to be included in the Editors’ Picks List.
Lastly, I am a husband and a father of two incredible sons. Oh, I enjoy drinking copious amounts of coffee, too.
Dana C. Ernst, PhD
Department of Mathematics & Statistics
Northern Arizona University
805 South Osborne Drive
PO Box 5717
Flagstaff, AZ 86011
Note: The views expressed on this blog are my own and are not necessarily shared by my employer Northern Arizona University.