Associate Professor, Mathematics
Frable, 201H
Penn State Greater Allegheny, 4000 University Drive, McKeesport, PA 15132
Biography
I am an Associate Professor at Penn State Greater Allegheny. Before coming to
Penn State, I was a Visiting Assistant Professor at Smith College and University
of California, Riverside.
Research Interests
My primary research focuses on commutative algebra and its connection to
algebraic geometry and combinatorics. More specifically, I work on defining
questions of blow-up algebras as well as various invariants of varieties.
Applications of my research include coding theory, geometry modeling, chemical
reaction networks, optimization problems, and permutation statics. Other than
working on pure mathematics and its applications, I am interested in finding the
impact of the usage of technology in mathematics classrooms.
Publications
- Rees algebras of sparse determinantal ideals, with E. Celikbas, E. Dufresne, L. Fouli, E. Gorla, C. Polini, and I. Swanson. To appear Transactions of the American Mathematical Society.
- Regularity and Multiplicity of Toric Rings of Three-dimensional Ferrers Diagrams, with Y.-H. Shen, Journal of Algebraic Combinatorics Vol. 57 (2023),1073-1101.
- Symbolic Powers and Free Resolutions of Generalized Star Configurations of Hypersurfaces, with Y.-H. Shen, Michigan Mathematical Journal Vol. 73 (2023), 33–66.
- Blow-up algebras of secant varieties of rational normal scrolls, with Y.-H. Shen, Collectanea Mathematica Vol. 74 (2023), 247-278.
- Multi-Rees Algebras and Toric Dynamical Systems, with D. Cox and G. Sosa, Proceedings of the American Mathematical Society, Vol. 147, No. 11 (2019), 4605-4616.
Education
Ph.D., Purdue University
Papers and Presentations
- Algebra Seminar, New Mexico State, Apr. 2023
- Department of Mathematical Colloquium, NTHU Taiwan, Mar. 2023
- Combinatorial Number Theory Seminar, UC Riverside, Feb. 2023
- Algebraic Geometry Seminar, Cornell University, Oct. 2022
- Department of Mathematical Colloquium, Colgate University, Oct. 2022