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Dana Ernst

0000-0002-0663-4982

Assistant Professor (Mathematical sciences)

Northern Arizona University

I am an assistant professor in the Department of Mathematics and Statistics at Northern Arizona University in Flagstaff, AZ. 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. 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. Furthermore, I am passionate about mathematics education. In particular, I am interested in inquiry-based learning (IBL) and the Moore method for teaching mathematics. This educational paradigm has transformed my teaching. 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.

Publications

  • D.C. Ernst, A. Hodge, A. Schultz. Enhancing Proof Writing via Cross-Institutional Peer Review. (Accepted to PRIMUS)
  • B. Beaudrie, D.C. Ernst, B. Boschmans. Redesigning an Algebra for Precalculus Course. In T. Bastiaens & G. Marks (Eds.), Proceedings of World Conference on E-Learning in Corporate, Government, Healthcare, and Higher Education, 2013. Chesapeake, VA: AACE.
  • B. Beaudrie, B. Boschmans, and D.C. Ernst. First Semester Experiences in Implementing a Mathematics Emporium Model. In R. McBride & M. Searson (Eds.), Proceedings of Society for Information Technology & Teacher Education International Conference, 2013. Chesapeake, VA: AACE.
  • D.C. Ernst. Diagram calculus for a type affine C Temperley-Lieb algebra, I. J. Pure Appl. Alg. 216(11), 2012. [arXiv:0910.0925]
  • T. Boothby, J. Burkert, M. Eichwald, D.C. Ernst, R.M. Green, and M. Macauley. On the Cyclically Fully Commutative Elements of Coxeter Groups. J. Algebraic Combin. 36(1), 2012. [arXiv:1202.6657]
  • D.C. Ernst. Non-cancellable elements in type affine C Coxeter groups, Int. Electron. J. Algebra 8, 2010. [arXiv:0910.0923]
  • D.C. Ernst. A diagrammatic representation of an affine C Temperley–Lieb algebra, PhD Thesis, University of Colorado, 2008. [arXiv:0905.4457]
  • D.C. Ernst. Cell Complexes for Arrangements with Group Actions, MS Thesis, Northern Arizona University, 2000. [arXiv:0905.4434]
  • B. Love, A. Hodge, C. Corritore, and D.C. Ernst. Inquiry-Based Learning and the Flipped Classroom Model. (Submitted)
  • D.C. Ernst, M. Leingang, and R. Taylor. To friend or not to friend? Facebook for professional educators. (Submitted)
  • B. Beaudrie, D.C. Ernst, E. Kennedy, and R. St. Laurent. A Flipped Classroom Study in Second Semester Calculus. (Submitted)
  • D.C. Ernst and A. Hodge. Within ϵ of Independence: An Attempt to Produce Independent Proof-Writers via IBL. (Submitted)
  • D.C. Ernst. Diagram calculus for a type affine C Temperley–Lieb algebra, II. [arXiv:1101.4215] (In Preparation)
  • D.C. Ernst, R.M. Green, M. Macauley, and N. Sieben. A combinatorial proof the CFC elements are logarithmic. (In Preparation)
  • D.C. Ernst, M. Hastings, and S. Salmon. Factorization of Temperley-Lieb diagrams. (In Preparation)
  • D.C. Ernst and D. Jacobson. Optimizing Solutions of 2×2 Spinpossible boards. (In Preparation)
  • B. Beaudrie, D.C. Ernst, E. Kennedy, and R. St. Laurent. A Flipped Classroom Study in Third Semester Calculus. (In Preparation)
  • D.C. Ernst and N. Sieben. Impartial games for generating groups. (In Preparation)

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