My research is in algebraic geometry, inspired in part by theoretical physics. My research interests include enumerative geometry (Gromov-Witten and Donaldson-Thomas invariants), moduli spaces, tropical geometry, mirror symmetry and non-commutative algebra.
My research is partially supported by the NSF grant Dualities in Enumerative Algebraic Geometry, DMS 2302117
Preprints:
Non-toric brane webs, Calabi-Yau 3-folds, and 5d SCFTs, joint with Valery Alexeev and Hülya Argüz, 2024. Video
The KSBA moduli space of stable log Calabi-Yau surfaces, joint with Valery Alexeev and Hülya Argüz, 2024. Video
All-genus WDVV recursion, quivers, and BPS invariants, joint with Longting Wu, 2023.
Quivers, Flow Trees, and Log Curves, joint with Hülya Argüz, 2023. Video
Published papers at peer-reviewed journals:
Quivers and curves in higher dimension, joint with Hülya Argüz, to appear at Transactions of the American Mathematical Society 2024.
Holomorphic Floer theory and Donaldson-Thomas invariants, published in String-Math 2022, Proceedings of Symposia im Pure Mathematics 2024. Video Slides
BPS Dendroscopy on Local P2, joint with Pierre Descombes, Bruno Le Floch, and Boris Pioline, published in Communications in Mathematical Physics 2024. Video Slides
Fock-Goncharov dual cluster varieties and Gross-Siebert mirrors, joint with Hülya Argüz, published in Journal für die reine und angewandte Mathematik (Crelles Journal) 2023. Video Slides
Gromov-Witten theory of Complete Intersections via Nodal Invariants, joint with Hülya Argüz, Rahul Pandharipande, and Dimitri Zvonkine, published in Journal of Topology 2023. Videos 1,2, and 3
The flow tree formula for Donaldson-Thomas invariants of quivers with potentials, joint with Hülya Argüz, published in Compositio Mathematica 2022. Videos 1 and 2 Slides
Stable maps to Looijenga pairs: orbifold examples, joint with Andrea Brini and Michel van Garrel, published in Letters in Mathematical Physics 2021.
Stable maps to Looijenga pairs, joint with Andrea Brini and Michel van Garrel, published in Geometry and Topology 2024.
Strong positivity for the skein algebras of the 4-punctured sphere and of the 1-punctured torus, published in Communications in Mathematical Physics 2022. Video Slides
Real Log Curves in Toric Varieties, Tropical Curves, and Log Welschinger Invariants, joint with Hülya Argüz, published in Annales de l'Institut Fourier 2022.
Scattering diagrams, sheaves, and curves, published in Acta Mathematica Sinica, English Series 2021.
Holomorphic anomaly equation for (P2,E) and the Nekrasov-Shatashvili limit of local P2, joint with Honglu Fan, Shuai Guo, and Longting Wu, published in Forum of Mathematics, Pi 2021. Video Slides
A proof of N.Takahashi's conjecture for (P2,E) and a refined sheaves/Gromov-Witten correspondence, published in Duke Mathematical Journal 2023.
Scattering diagrams, stability conditions, and coherent sheaves on P2 , published in Journal of Algebraic Geometry 2022.
On the log-local principle for the toric boundary, joint with Andrea Brini and Michel van Garrel, published in Bulletin of the London Mathematical Society 2022.
Refined floor diagrams from higher genera and lambda classes, published in Selecta Mathematica 2021.
On an example of quiver DT/relative GW correspondence, published in International Mathematics Research Notices 2020.
Quantum mirrors of log Calabi-Yau surfaces and higher genus curve counting, published in Compositio Mathematica 2020.
The quantum tropical vertex, published in Geometry and Topology 2020.
Tropical refined curve counting from higher genera and lambda classes, published in Inventiones Mathematicae 2018.