My doctoral dissertation is in commutative algebra, but I have broad mathematical interests. In the past several years, I've also worked on research projects in graph theory, combinatorics, mathematical games, topology, and voting theory. I most enjoy projects that I can work on with students. In some of my past lives, I was a gymnast and a chemist. Someday, I would like to partner with chemistry faculty on projects in the nontrivial intersection between chemistry and mathematics. My goal in the classroom is to have students doing mathematics in class, instead of watching me do mathematics. This means I use inquiry-based learning strategies in a variety of ways in my classrooms.
I. Asplund-Wain, G. Dojan, C. Griffin, K. Ikard, S. Kniahnitskaya, A. Mallott, B. Nored, K. Shultis, C. Stainsby, H. Whitlatch. Total Roman Domination of Kneser Graphs. In progress.
N. Hari, M. Orrison, K. Shultis, J. Sorrells. Quadratic Voting. In progress.
S. Kniahnitskaya, O. Ramirez, M. Ortiz, K. Shultis, H. Whitlatch. Counting Power Domination Sets in Complete m−ary Trees. Theory and Applications of Graphs, 10(1), 2023.
T. DeGiovanni, J. Lutz, K. Shultis. Economical Dissections. Recreational Mathematics Magazine, Vol. 10, 2023.
K. Shultis. What Counts as Math Research? Council on Undergraduate Research, Mathematics, Computer Science, and Statistics Blog, 2022.
K. Shultis, P. Thompson. Reducibility of parameter ideals in low powers of the maximal ideal, Commutative Algebra, Contemporary Mathematics, vol. 773, Amer. Math. Soc., Providence, RI, 2021, pp. 181-193.
V. Coufal, K. Shultis. Integration Techniques. The Journal of Inquiry Based Learning in Mathematics, No. 2, 2021.
K. Shultis. Systems of parameters and the Cohen Macaulay property. J. Commut. Algebra, 10(1):139-151, 2018.
Y. Tian, M. Kayatta, K. Shultis, A. Gonzalez, L. J. Mueller, M. E. Hatcher. 31P NMR Investigation of Backbone Dynamics in DNA Binding Sites. The Journal of Physical Chemistry B 113 (2009), no. 9, 2596-2603, DOI 10.1021/jp711203m.
K. Shultis, Systems of parameters and the Cohen-Macaulay property. (accepted to the Journal of Commutative Algebra)
Ye Tian, Michael Kayatta, Katharine Shultis, Alejandro Gonzalez, Leonard J. Mueller, Mary E. Hatcher, 31P NMR Investigation of Backbone Dynamics in DNA Binding Sites. The Journal of Physical Chemistry B 113 (2009), no. 9, 2596-2603, DOI 10.1021/jp711203m.