Research
My research is in algebraic geometry. My interests concern enumerative invariants arising from intersection theory on moduli spaces. More specifically, most of my research focuses on (logarithmic) Gromov-Witten invariants, as well as quasimap theory.
Publications/Preprints
Refined curve counting with descendants and quantum mirrors, with Patrick Kennedy-Hunt and Ajith Urundolil Kumaran, [arXiv:2502.17236].
Crepant Transformation Conjecture For the Grassmannian Flop, with Wendelin Lutz and Rachel Webb, to appear in Transactions of the AMS, [arxiv:2404.12302].
The local/logarithmic correspondence and the degeneration formula for quasimaps, with Alberto Cobos Rabano and Cristina Manolache, [arxiv:2404.01381].
Tropical refined curve counting with descendants, with Patrick Kennedy-Hunt and Ajith Urundolil Kumaran, Communications in Mathematical Physics, Volume 405, no. 240 (2024), [arXiv:2307.09436], [journal].
Logarithmic quasimaps, Advances in Mathematics, Volume 438 (2024), [arXiv:2301.01196], [journal].
Divisors and curves on logarithmic mapping spaces, with Patrick Kennedy-Hunt, Navid Nabijou and Wanlong Zheng, Selecta Mathematica, Volume 30, no. 75 (2024), [arxiv:2209.00630], [journal].
The abelian/non-abelian correspondence and Gromov-Witten invariants of blow-ups, with Tom Coates and Wendelin Lutz,
Forum of Mathematics, Sigma , Volume 10 , e67 (2022), [arXiv:2108.10922],[journal].
Talk notes
Here are some notes, written by Parth Shimpi, based on a mini-course I gave in the UKAG Network Winter School (Warwick) on the Enumerative Geometry of (log) K3 Surfaces.
Here are some notes I wrote when giving a talk about excess intersections in the Imperial junior geometry seminar.
Here are some notes I wrote when giving a talk about moduli spaces in the Imperial junior geometry seminar.
Projects
In Spring 2019 I completed a mini-project together with Wendelin Lutz on Gromov-Witten Theory. This was a great reference.
In Spring 2019 I completed a mini-project together with Federico Bongiorno and Liam Stigant about equivalences of derived categories under flops following this article.