Research
Research
Research Interests
My research interests lie in the intersection of enumerative geometry and combinatorics. I am fond of working with toric varieties: I have been studying moduli spaces of logarithmic stable maps to toric surface pairs and the logarithmic quantum cohomology of toric surfaces. I make use of tropicalisation techniques and the combinatorial correspondances of toric geometry.
Preprints
We study moduli spaces of logarithmic stable maps to proper toric surfaces with prescribed tangency conditions to the toric boundary. Fixing a surface, we define a chamber decomposition on the space of all tangencies such that as a function of the tangency data, the class of the corresponding moduli space in the Grothendieck ring of varieties is constant. The tangency data defines a collection of lines through the origin which, along with the rays of the toric fan, are cyclically ordered. The chambers of the decomposition are regions for which this cyclic ordering is constant and generalise the well-known resonance chambers. We pose the open question of whether the Gromov-Witten invariants of the moduli spaces are polynomial on these chambers.
Posters & Slides
My most recent poster for QMUL PGR Day 2025 can be found here.
I also presented a poster at the GAP XIX conference in Rome back in September 2024 which can be found here.
See here for the slides of my talk at WINGs 2025!
Toric Geometry Notes
I have typed up Navid's lecture notes for the Toric Geometry course he gave at the University of Cambridge. Here they are! (Corrections appreciated)