Research

My research interests are in algebraic geometry, and its connections with fields such as algebra and combinatorics.

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:

Geometry over the field with one element, see here (survey by Oliver).
Tropical scheme theory, see here (lecture note by Oliver).
Invitation to hyperrings and hyperfields (survey by me, coming soon!) - for the current version, see here (as of Aug 2022).

Conference Organized

(Upcoming) 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)

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)

(2020, 2023) On the Hopf algebra of multi-complexes slides (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).