Research and Writings

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

• Crepant Transformation Conjecture For the Grassmannian Flop, with Wendelin Lutz and Rachel Webb, [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, [arXiv:2307.09436].

• 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, to appear in Selecta Mathematica, [arxiv:2209.00630].

• 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.