Research

This page contains information about my current research interests and activity.

Research Interests

My main interests in mathematical research fall under the wide umbrella of representation theory of Lie algebras. This leads me to spending a majority of my time working with enveloping algebras and their deformations.

Additionaly, I am interested in studying the teaching and learning of mathematics as a whole. I have worked on projects involving college readiness of students and understanding student perspectives about their mathematical ability. This is an area I hope to continue to grow with my current institutions focus on undergraduate education.

You can find an in-depth discussion of my current research in my research statement.

Papers

  1. Structure of Galois rings and the Gelfand-Kirillov Conjecture w/ Vyacheslav Futorny, Jonas T. Hartwig, & João Schwarz [arXiv]
  2. Hilbert-Samuel Polynomials for Algebras with Special Filtrations w/ Jonas T. Hartwig & João Schwarz (Submitted) [arXiv]
  3. Maps Between Standar and Principal Orders (Submitted)[arXiv]
  4. A study of Galois and flag orders (Thesis) [Abstract][PDF]
  5. An Extension of U(gln ) Related to the Alternating Group and Galois Orders (In Journal of Algebra)

Grants & Awards

  • Buschman Faculty Award from Westminster College (Missouri) - >$10,000
  • Missouri Section of MAA Project NExT Fellow 2024
  • College Preparedness Grant with Dr. Katrina Rothrock from NCTM & MET - $8,000
  • Student-Faculty Research Project Grant via ORSP at UWEC - $2,000
  • Aggie Ho Teaching Award 2019 from Iowa State University
  • Iowa State University Teaching Excellence Award 2018

Research with Undergraduates

  • Improving College Readiness of Rural High School Seniors (Funded by MET grant & ORSP Internal Grant)
  • Standard flag orders for non-complex reflection groups (Funded by ORSP Interal Grant)

Conferences & Presentations

Spring 2025

  • Attended professional development at the Missouri MAA Sectional Meeting

    • Spring 2024

    • Inducted into the Missouri section of Project NExT at the Missouri MAA Sectional Meeting
    • Selected to present at the 56th Wisconsin Mathematics Council Annual Conference

    Fall 2023

    • Organized a Special Session at the AMS Southeastern Fall Sectional Meeting

    Spring 2023

    • Invited research presentation at Westminster College - Missouri [Slides]
    • Presented at the Joint Mathematics Meetings 2023 in the Contributed Paper Session [Slides]

    Spring 2022

    • Invited talk at the AMS Central Spring Sectional Meeting

    Spring 2021

    • Invited talk at the AMS Southeastern Spring Sectional Meeting [Slides]

    Spring 2020

    • Attended the Conference on Lie and Jordan Algebras, Their Representations and Applications in Chengdu, Sichuan, China (Conference Homepage) *Funded

    Fall 2019

    • Inivited talk at the University of Iowa Algebra Seminar [Slides]
    • Invited talk at the University of Texas at Arlington AGANT Seminar [Slides]
    • Invited talk at the University of South Alabama Mathematics Colloquium [Slides]
    • Invited talk at the St. Olaf College Mathematics Research Seminar [Slides]
    • Presented at the AMS Central Fall Sectional Meeting in the Contributed Paper Session [Slides]

    Summer 2019

    • Attended MSRI Summer School 850 - "Representation Stability" (Course Homepage) *Funded

    Spring 2019

    • Presented at the AMS Southeastern Spring Sectional Meeting in the Special Session on Geometric and Combinatorial Aspects of Representation Theory (Abstract) [Slides]
    • Attended Mini-Course at the Atlantic Algebra Centre St. John's, Newfoundland, Canada (Course Homepage) *Funded

    Fall 2018