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Research Interests
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, and characteristic p methods.
Publications
Publications
(Submitted) Weak Normalization of an Affine Semigroup, with K. Maddox. (2025).
(Submitted) Numerical Semigroups of Sally Type, with S. Dubey, K. Goel, N. Sahin, H. Srinivasan. (2025).
(Accepted) The Betti Numbers of Kunz-Waldi Semigroups, with M. Gonzalez and H. Srinivasan. (2025). Proceedings of the American Mathematical Society.
(Appeared) A class of Numerical Semigroups defined by Kunz and Waldi - their Principal Matrices and structure, with Hema Srinivasan. (2024). Journal of Algebra and its Applications.
(Appeared) Wilf Inequality is preserved under Gluing of Semigroups, with Hema Srinivasan. (2023). Journal of Algebra and its Applications.
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(In Preparation) Numerical Semigroups of Sally Type - Part II, with S. Dubey, K. Goel, N. Sahin, H. Srinivasan.
Thesis
Thesis
My thesis is a combination of two related works: First, I study 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. I have characterized the principal matrices of numerical semigroups in this class, and am now working on describing a minimal free resolution of the associated semigroup rings.
The second part involves 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.
Other Projects
Other Projects
In January 2025, I was at the 5-day Apprenticeship Program in Commutative Algebra at the Fields Institute, Toronto, Canada. Our group is working on problems related to non-standard graded Veronese rings.
In June 2024, I attended the 5-day Women in Commutative Algbera (III) workshop at Casa Matemàtica Oaxaca (CMO), Mexico. I was a part of the ‘Affine Semigroup and Associated Primes’ group. We study Numerical Semigroups of Sally Type, and are continuing the research started at the workshop.
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 crash courses in tropical and logarithmic geometry. We focused on practical applications in enumerative geometry and moduli theory, with insights into their connection with tropical and logarithmic geometry.
Recent Talks
Recent Talks
AMS Fall Sectional, Tulane University, New Orleans
-Special Session on Algebraic Combinatorics and Combinatorial Commutative Algebra
-Special Session on Syzygies and Local Cohomology in Commutative Algebra
October 3-5, 2025
SIAM Conference on Applied Algebraic Geometry; Minisymposium on Multigraded Structures: Castelnuovo-Mumford Regularity and Applications, University of Wisconsin-Madison
July 7-11, 2025
AMS Sectional; Special Session on Topics in Commutative Algebra, University of Kansas, Lawrence
March 29-30, 2025
Universidad de La Laguna Algebra Seminar (Online)
February 18, 2024
Algebra Seminar, University of Arkansas; Principal Matrices of a Class of Numerical Semigroups
November 15, 2024
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
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