My research interests are in algebraic geometry, and its connections with fields such as algebra and combinatorics. My work is supported by NSF LEAPS-MPS ($250,000, DMS-2532394) and AMS-Simons Research Enhancement Grants for Primarily Undergraduate Institution (PUI) Faculty.
Here are more specific topics that I am currently working on:
Tropical geometry; currently trying to find a proper notion of vector bundles in this setting.
Geometry over the field with one element F_1; quiver representations over F_1, coherent sheaves on monoid schemes, and Hall algebras obtained from them.
Various aspects of hyperfields and hyperfields, including geometry and combinatorics.
Combinatorial Hopf algebras and their relation to Hopf algebras.
Zeta functions in combinatorics.
Here are some survey papers providing an overview of research areas I'm working on:
AMS Eastern Sectional Meeting (University at Albany), Special Session: Matroids, quivers, F_1-geometry, and connections with algebra (Oct. 19-20, 2024) with C. Eppolito and A. Sistko
AMS Eastern Sectional Meeting (University at Buffalo), Special Session: Building bridges between F_1-geometry, combinatorics, and representation theory (Sep. 9-10, 2023) with C. Eppolito and A. Sistko
AMS Virtual Sectional Meeting (formerly at Georgia Tech), Special Session: Tropical Geometry, F_1-connections and Matroids (Mar. 13-14, 2021) with K. Mincheva
The F_1 World Seminar (with Oliver Lorscheid, Matt Szczesny, Koen Thas, and Matt Young)
NSF LEAPS-MPS ($250,000, DMS-2532394) - Commutative algebra of semirings through the lens of algebraic geometry and combinatorics, 2025 - 2027.
AMS-Simons Research Enhancement Grant for Primarily Undergraduate Institution (PUI) Faculty - Hall algebras in a non-additive setting and its relation to combinatorial Hopf algebras, 2023 - 2026.
Summer Undergraduate Research Experience grant (SUNY New Paltz), Summer 2022, Summer 2023
Research and Creative Projects Awards (SUNY New Paltz), 2020 - 2021, 2023-2024, 2024-2025
SIAM Early Career Travel Award
AMS -Simons Travel Grant, 2018 - 2020
AMS Travel Grant for attending ICM 2018 in Rio de Janeiro, Brazil (declined)
(2025) Tropical subrepresentations and matroids (talk give at the special seminar IAS) (click here)
(2020, 2023) On the Hopf algebra of multi-complexes slides (click here) and video (click here)
(2019) The Hall algebra of the category of matroids (my recorded talk, click here)
(2019) Category of matroids, Hopf algebras, and Hall algebras slides (click here)
(2017) Geometry of hyperfields slides (talk given at Boston University, here).
(2016) My talk at GMU is on Youtube (click here).
(2015) Thesis presentation file (click here).