Research Interests
I am doing research in Algebraic Topology under the supervision of Dr. Craig Westerland. Specifically, I am studying topics related to Arithmetic Statistics, Braid Groups, Quantum Shuffle Algebras, and Nichols Algebras. An expository paper describing some of these topics that I used for my Master defense can be found below.
Braid Group Homologies, Quantum Shuffle Algebra Cohomologies, and Fomin Kirillov Algebras.
In preparation for my oral exam and master degree defense, Michael C. Loper and I wrote a study guide detailing the topics covered in MATH 8245: Group Theory as taught by Peter Webb in 2015-2016. These topics include wreath products, group cohomology, crystallography, and a number of other topics. This study guide is included below.
In Summer 2019, I helped to supervise a Combinatorics research group as a part of the University of Minnesota Summer REU (Research Experience for Undergraduates). The arXiv publication of our results is included below.
In my final year at Carleton College, I completed my Senior Comprehensive exercise under the supervision of Dr. Eric Egge. We studied Doubly-Alternating Baxter Permutations and Tilings of Aztec Diamonds. The publication of our results can be found below.
Domino tilings of Aztec diamonds, Baxter permutations, and snow leopard permutations.
I participated in an REU with the Math department at Iowa State University alongside Dr. Sung-Yell Song. We researched the Cayley-Isomorphism Property of finite groups and introduced the notion of a group being "Irreducibly Non-CI." Slides from a presentation I gave on this topic can be found here.
