Structures in topological recursion relations
in "Transactions of the American Mathematical Society Series B" 12 (2025), 1223-1263
Research
My expertise lies in algebraic geometry, and I work on problems inspired by string theory. I study moduli spaces of algebraic curves, maps, etc. with applications to Gromov-Witten theory and strata of holomorphic differentials. During my PhD, my focus was the study of tautological classes on the moduli space of curves. My current focus is to further lay the foundations of the geometric technique "log GLSM", and to study its applications.Publications/Preprints (authors listed in alphabetical order)
Gromov-Witten Invariants of Non-Convex Complete Intersections in Weighted Projective Stacks
submitted
arXiv ·
Universal equations for higher genus Gromov-Witten invariants from Hodge integrals
in "Communications in Mathematical Physics", Volume 405, article number 47, (2024)
Gromov-Witten invariants with naive tangency conditions
in "International Mathematics Research Notices" Volume 2025, Issue 20, October 2025, rnaf310
Structural formulae in logarithmic Gauged Linear Sigma Models II: Effective invariants and cycles
submitted
arXiv ·
Virtual cycles of stable (quasi-)maps with fields
in "Advances in Math" Volume 385, 16 July 2021, Art. No. 107781, 49pp
The logarithmic gauged linear sigma model
in "Inventiones mathematicae", 225(3), 1077-1154, 2022
Double ramification cycles with target varieties
in "Topology" Volume 13 Issue 4, December 2020, Pages 1725--1766
Towards Logarithmic GLSM: The $r$-spin case
in "Geometry and Topology" Issue 26-7, 2022, Pages 2855--2939
Higher-genus wall-crossing in the gauged linear sigma model
in "Duke Mathematical Journal" 170 (4), 697-773, (15 March 2021)
Topological recursion relations from Pixton's formula
in "Michigan Math Journal" 73 (2023), 227-241
Higher-genus quasimap wall-crossing via localization
in "Algebraic Geometry" (Foundation Compositio Mathematica) 11 (5) (2024) 712--736
Appendix: Holomorphic differentials
in "Tautological relations via r-spin structures" by Rahul Pandharipande, Aaron Pixton and Dimitri Zvonkine in "Journal of Algebraic Geometry" 28 (2019), 439--496
Powers of the theta divisor and relations in the tautological ring
in "International Mathematics Research Notices" Volume 2018 Issue 24, 12 December 2018, Pages 7725--7754
Double ramification cycles on the moduli space of curves
in "Publications mathématiques de l'IHÉS" 125 (2017), 221--266
Pixton's double ramification cycle relations
in "Geometry and Topology" 22-2 (2018), 1069--1108
Relations on $\overline M_{g,n}$ via equivariant Gromov-Witten theory of $\mathbb P^1$
in "Algebraic Geometry" (Foundation Compositio Mathematica) Volume 4, Issue 3 (May 2017), 311--336
Appendix: The weighted fundamental class of $\widetilde{\mathcal H}_g(\mu)$
in "The moduli space of twisted canonical divisors" by Gavril Farkas and Rahul Pandharipande in "Journal of the Institute of Mathematics of Jussieu" Volume 17, Issue 3 (June 2019), 615--672
Frobenius Manifolds near the Discriminant and Relations in the Tautological Ring
part of PhD thesis, in "Letters in Mathematical Physics" 108 (2018), no 7, 1649--1675
The hypergeometric functions of the Faber-Zagier and Pixton relations
in Pure and Applied Mathematics Quarterly Volume 11 (2015), Number 4 (Special volume dedicated to Prof. Eduard Looijenga), 591--631
Comparing tautological relations from the equivariant Gromov-Witten theory of projective spaces and spin structures
part of PhD thesis
arXiv ·
Gromov-Witten theory of target curves and the tautological ring
in Michigan Mathematical Journal, Volume 66, Issue 4 (2017), (683--698)
Socle pairings on tautological rings
in Epijournal de Géométrie Algébrique, Volume 3 (2019), Article no. 4
Gaussian rational points on a singular cubic surface
in "Torsors, étale homotopy and applications to rational points", LMS Lecture Notes 405, Cambridge University Press, Cambridge, 2013, pp. 210-231
In preparation
"Structural formulae in logarithmic Gauged Linear Sigma Models I: The tropical decomposition formula" (with Qile Chen and Yongbin Ruan), working draft
"Structural formulae in logarithmic Gauged Linear Sigma Models II: Effective invariants and cycles" (revision of arXiv:2208.04519, with Qile Chen and Yongbin Ruan)
"Structural formulae in logarithmic Gauged Linear Sigma Models III: The localization formula" (with Qile Chen and Yongbin Ruan)