Research

My current research area is Computational Commutative Algebra and Algebraic Geometry.

I recently used Liaison theory to prove a Grobner basis result for the defining ideal of Schubert patch varieties, thereby, recovering some known results (e.g. Grobner basis) of the Kazhdan-Lusztig ideals, and hence, the Schubert determinantal ideals – the defining ideals for the matrix Schubert varieties.

I plan to use this same technique (liaison theory) to show that the set of generators for the defining ideal of certain quiver loci is a Grobner basis.

Paper

A Grobner Basis for Schubert Patch Ideals, Journal of Algebra, Volume 634, 15 November 2023, Pages 165-208.
doi.org/10.1016/j.jalgebra.2023.06.039
arXiv:2111.13778

Thesis

Grobner Bases Via Linkage for Classes of Generalized Determinantal Ideals. A Dissertation Submitted to the College of Graduate and Postdoctoral Studies in Partial Fulfillment of the Requirements for the degree of Doctor of Philosophy (PhD) in the Department of Mathematics and Statistics of College of Arts and Science, University of Saskatchewan
Canonical Forms for Matrices over Polynomial Rings. A Thesis Submitted to the College of Graduate and Postdoctoral Studies in Partial Fulfillment of the Requirements for the degree of Master of Science (M.Sc.) in the Department of Mathematics and Statistics, University of Saskatchewan
Exploring the relation between ideals and varieties. A research project submitted to the African Institute for Mathematical Sciences (AIMS), South Africa; in partial fulfillment of a structured Master degree (M.Sc.) in Mathematical Sciences

Page updated

Report abuse