This page contains information about my current research interests and activity.
Research Interests
My main interests 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.
I am currently working with Jonas Hartwig to describe a Galois or Flag order realization of U(son) related to the realization for U(gln). I am also interested in Galois/Flag orders related to the Alternating group. As most work in the field is focused on complex reflection groups, there are many interesting unexplored directions for non-reflection groups.
You can find an in-depth discussion of my current research in my research statement.
Papers
- Hilbert-Samuel Polynomials for Algebras with Special Filtrations w/ Jonas T. Hartwig & João Schwarz (In Preparation)
- Maps Between Standar and Principal Orders (Submitted)[arXiv]
- A study of Galois and flag orders (Thesis) [Abstract][PDF]
- An Extension of U(gln ) Related to the Alternating Group and Galois Orders (In Journal of Algebra)
Undergraduate Projects
- Standard flag orders for non-complex reflection groups (Funded by ORSP Interal Grant)
Conferences & Presentations
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
