Research

My research interests lie in the intersection of algebraic and tropical geometry. Currently, I am studying a class of spaces called projectivized toric vector bundles with the hope of identifying a new class of Mori dream spaces.

Research Statement

Please find a copy of my research statement here.

Publications

Algebra and Geometry of irreducible toric vector bundles of rank n on P^n, with Christopher Manon

Positivity properties of divisors on toric vector bundles, with Christopher Manon

Cox rings of projectivized toric vector bundles and toric flag bundles, with Christopher Manon

Spectral properties of graphs associated to the Basilica group, with Antoni Brzoska, Samantha Jarvis, Luke G. Rogers, and Alexander Teplyaev

Counting odd numbers in truncations of Pascal’s triangle, with Robert G. Donnelly, Molly W. Dunkum, and Stefan Schnake

Thesis

My thesis, Toric Bundles as Mori Dream Spaces, can be found here.

Parts of the project were largely supported by code I'd written in Macaulay2. These functions are currently being generalized for wider application and a link to the github will be posted as soon as they are available.