Publications/Upcoming Publications
- G-groups of Cohen-Macaulay rings with n-Cluster Tilting Objects
- A Generalization of Wilf's Conjecture for Numerical Semigroups (with Carmelo Cisto, Michael Dipasquale, Gioia Failla, Chris Peterson, and Rosanna Utano)
- The Apolar Algebra of a Product of Linear Forms (with Michael DiPasquale and Chris Peterson)
- On the Weak Lefschetz Property for Vector Bundles on \(\mathbb{P}^2\) (with Chris Peterson and Gioia Failla)
Broadly, I am interested in applying geometric and topological techniques to study finitely generated modules over Noetherian rings, most often in the graded and local cases. In the local case I am interested in studying certain Quillen K-groups for the category of finitely generated modules. In the graded case, I am interested in studying Lefschetz properties for finite length modules over a polynomial ring and in studying the structure of annihilators of families of forms (e.g. hyperplane arrangements).
For a really great and brief introduction to the history and motivation for K-theory, check out "Attitudes of K-theory: Topological, Algebraic, and Combinatorial", by Inna Zakharevich. For a slightly less brief but just as fantastic introduction to Lefschetz properties, check out "A Tour of the Weak and Strong Lefschetz Properties" by Juan Migliore and Uwe Nagel.
For a really great and brief introduction to the history and motivation for K-theory, check out "Attitudes of K-theory: Topological, Algebraic, and Combinatorial", by Inna Zakharevich. For a slightly less brief but just as fantastic introduction to Lefschetz properties, check out "A Tour of the Weak and Strong Lefschetz Properties" by Juan Migliore and Uwe Nagel.
Pictured: The Crestone group from the summit of of Humboldt Peak (14, 064') and my favorite orange jacket in September 2016.