I am highly interested in Algebra and Combinatorics and where the two meet. Combinatorial Representation Theory is the area in which I am currently working. I do have a background in Statistics and Probability, but Representation Theory stole my heart.
Specifically, I am working with Representation Theory of Lie algebras. Under the guidance of my advisor, Vyjayanthi Chari, I am working toward finding the graded characters of highest weight modules over type D Current algebras. This is based of of the work of R. Biswal, V. Chari, P. Shereen, and J. Wand published in January of 2020 on arXiv, Macdonald Polynomials and Level Two Demazure Modules for Affine sln+1 . The goal of my research is to find ways to express the graded characters of generalized Demazure modules indexed by two weights in terms of well-studied polynomials in the same fashion as my advisor and her team. The planned extension of this work would be to relax the conditions surrounding the results, or extend to generalized Demazure modules indexed by more than two weights.
The point of working with these representations over these Current algebras is that the Current algebra is a maximal parabolic subalgebra of the Affine Lie algebra, making it possible to translate the results back to the Affine case. These representations are highest weight in these settings, and so we learn a great deal about the affine algebra from the knowledge of these representations.
Women in Representation Theory, Attendee. Online through Zoom, UC Los Angeles (May 2021)
Discussion Meeting on Representation Theory, Attendee. Online through Zoom, Indian Institute of Science (December 2020)
Underrepresented Students in Topology and Algebra Research Symposium, Accepted Speaker. Cancelled due to pandemic. University of Iowa (March 2020)
Geometry and Representation Theory, Attendee. UC Riverside (December 2019)
AMS Fall Western Sectional Meeting, Attendee. UC Riverside (November 2019)
Math Connections Graduate Student Seminar, Attendee. UC Riverside (May 2019)
Southeastern Lie Theory Workshop XI, Attendee. Louisiana State University, Baton Rouge, LA. Funding provided by conference. (May 2019)
AMS Spring Central and Western Joint Sectional Meeting, Attendee. University of Hawai’i at Mānoa. Funding Provided by UC Riverside. (March 2019)
Math Connections Graduate Student Seminar, Attendee. UC Riverside (May 2018)
Joint Mathematics Meetings, Attendee. San Diego Convention Center (January 2018)
AMS Fall Western Sectional Meeting, Attendee. UC Riverside (November 2017)
Math Connections Graduate Student Seminar, Attendee. UC Riverside (May 2017)