Research
Research Interests
My research focuses on affine semigroups, approaching the study through commutative algebra techniques involving semigroup rings, especially their minimal resolutions, and combinatorics. I have worked extensively with principal matrices, gluing of affine semigroups, and Wilf’s Conjecture for higher dimensional finitely generated affine monoids. I have also examined thoroughly subjects such as convex polytopes, the the koszul complex, Zariski’s main theorem, and the general theory of Cohen-Macaulay rings.
In one of my two ongoing projects, I am exploring a class of numerical semigroups constructed geometrically by Kunz and Waldi, and a significant matrix type linked to these semigroups, introduced by my advisor, Dr. Hema Srinivasan, and Dr. Papri Dey. These matrices offer valuable insights into the numerical semigroup while also possessing practical applications in both algebraic geometry and combinatorics.
My second active project involves the gluing of affine semigroups and addresses the notable, yet still open, conjecture of Wilf that establishes an inequality between three fundamental invariants of a numerical semigroup. Recently, we demonstrated that Wilf's inequality is preserved under this gluing process. I am currently working on generalizing these findings to higher dimensions using polyhedra and cones.
In other research-related news, I won the Raymond White Dissertation Year Fellowship for AY 2023-24. You can read about it here.
Publications
(Preprint) A class of Numerical Semigroups defined by Kunz and Waldi - their Principal Matrices and structure, with Hema Srinivasan.
(Accepted) Wilf Inequality is preserved under Gluing of Semigroups, with Hema Srinivasan.
From August 1-12, 2022, I was at St. Mary's College, California for the MSRI Tropical Geometry Summer School. This two-week program provided intensive crash courses in tropical and logarithmic geometry. We focused on practical applications in enumerative geometry and moduli theory, with valuable insights into their connection with tropical and logarithmic geometry.
Recent Talks
Upcoming Researchers in Commutative Algebra (URiCA), University of Nebraska, Lincoln;
May 11, 2024
Science on Tap, Columbia, Missouri; What is a Numerical Semigroup?
February 29, 2024
Algebra Seminar, University of Edinburgh; Wilf's Conjecture and More (and Less)
December 15, 2023
Graduate Seminar, University of Missouri-Columbia; Wilf's Conjecture 101
October 20, 2023
KUMUNU, University of Missouri-Columbia; Wilf's Conjecture and More (and Less)
September 23, 2023
Algebra Seminar, University of Missouri-Columbia; Wilf's Conjecture and More (and Less)
September 11, 2023
Graduate Seminar, University of Missouri-Columbia; Introduction to Tropical Geometry
October 14, 2022
Preprint Seminar, University of Missouri-Columbia; Exposition of 'A Bit of Tropical Geometry' by Brugallé and Shaw
October 12, 2022
Commutative Algebra Regional Expository Seminar (CARES), Numerical Semigroups and Wilf's Classification
November 16, 2022
Algebra Seminar, University of Missouri-Columbia; Deviation and Type of a Class of Numerical Semigroups
November 8, 2022