Research

My general research area is moduli spaces in algebraic geometry. I study moduli spaces of curves, maps and related ones with applications to Gromov-Witten theory and strata of holomorphic differentials. During my PhD, my main focus has been on the study of tautological classes on the moduli space of curves. My current focus is on developing the geometric technique of "log GLSM", and to study its applications.

Publications/Preprints

All of my articles are available on the arXiv.
Structure results for torus fixed loci (with Jarod Alper)arXiv submitted
Universal equations for higher genus Gromov-Witten invariants from Hodge integrals (with Xin Wang)arXiv DOI in "Communications in Mathematical Physics", Volume 405, article number 47, (2024)
Gromov-Witten invariants with naive tangency conditions (with Tony Yue Yu)arXiv submitted
Punctured Logarithmic R-maps (with Qile Chen and Yongbin Ruan)arXiv submitted
A comparison of group testing architectures for COVID-19 testing (with Joshua Batson, Yaim Cooper, Nathaniel Bottman)arXiv
Virtual cycles of stable (quasi-)maps with fields (with Qile Chen and Rachel Webb)arXiv DOI in "Advances in Math" Volume 385, 16 July 2021, Art. No. 107781, 49pp
The logarithmic gauged linear sigma model (with Qile Chen and Yongbin Ruan)arXiv DOI in "Inventiones mathematicae", 225(3), 1077-1154, 2022
Structure of Higher Genus Gromov-Witten invariants of Quintic 3-folds (with Shuai Guo and Yongbin Ruan)arXiv
Double ramification cycles with target varieties (with Rahul Pandharipande, Aaron Pixton and Dimitri Zvonkine)arXiv DOI in "Topology" Volume 13 Issue 4, December 2020, Pages 1725--1766
Towards Logarithmic GLSM: The $r$-spin case (with Qile Chen, Yongbin Ruan and Adrien Sauvaget)arXiv DOI in "Geometry and Topology" Issue 26-7, 2022, Pages 2855--2939
A mirror theorem for genus two Gromov-Witten invariants of quintic threefolds (with Shuai Guo and Yongbin Ruan)arXiv
Higher-genus wall-crossing in the gauged linear sigma model (with Emily Clader and Yongbin Ruan)arXiv DOI in "Duke Mathematical Journal" 170 (4), 697-773, (15 March 2021)
Topological recursion relations from Pixton's formula (with Emily Clader, Xin Wang and Dmitry Zakharov)arXiv DOI in "Michigan Math Journal" 73 (2023), 227-241
Higher-genus quasimap wall-crossing via localization (with Emily Clader and Yongbin Ruan)arXiv accepted at "Algebraic Geometry" (Foundation Compositio Mathematica)
Appendix: Holomorphic differentials (with Rahul Pandharipande, Aaron Pixton and Dimitri Zvonkine)arXiv DOI 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 (with Emily Clader, Samuel Grushevsky and Dmitry Zakharov)arXiv DOI in "International Mathematics Research Notices" Volume 2018 Issue 24, 12 December 2018, Pages 7725--7754
Double ramification cycles on the moduli space of curves (with Rahul Pandharipande, Aaron Pixton and Dimitri Zvonkine)arXiv DOI in "Publications mathématiques de l'IHÉS" 125 (2017), 221--266
Pixton's double ramification cycle relations (with Emily Clader)arXiv DOI in "Geometry and Topology" 22-2 (2018), 1069--1108
Relations on $\overline M_{g,n}$ via equivariant Gromov-Witten theory of $\mathbb P^1$arXiv DOI in "Algebraic Geometry" (Foundation Compositio Mathematica) Volume 4, Issue 3 (May 2017), 311--336
Appendix: The weighted fundamental class of $\widetilde{\mathcal H}_g(\mu)$ (with Rahul Pandharipande, Aaron Pixton and Dimitri Zvonkine)arXiv DOI 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 RingarXiv DOI 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 (with Alexandr Buryak and Rahul Pandharipande)arXiv DOI 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 structuresarXiv part of PhD thesis
Gromov-Witten theory of target curves and the tautological ringarXiv DOI in Michigan Mathematical Journal, Volume 66, Issue 4 (2017), (683--698)
Tautological relations in moduli spaces of weighted pointed curvesarXiv part of PhD thesis
Socle pairings on tautological rings (with Aaron Pixton)arXiv DOI in Epijournal de Géométrie Algébrique, Volume 3 (2019), Article no. 4
Gaussian rational points on a singular cubic surface (with Ulrich Derenthal)arXiv DOI 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 II: The localization formula" (with Qile Chen and Yongbin Ruan)
"Structural formulae in logarithmic Gauged Linear Sigma Models I: Tropical Geometry" (with Qile Chen and Yongbin Ruan)
"Gromov-Witten Invariants of Non-Convex Complete Intersections in Weighted Projective Stacks" (with Nawaz Sultani and Yang Zhou)

Thesis

My PhD thesis under the supervision of R. Pandharipande at ETH Zürich)

Funding

My research has been supported by NSF grants DMS-1901748, DMS-2054830 and DMS-2239320.