Research

My research is on enumerative aspects of algebraic geometry, in particular Gromov-Witten theory.

1. Higher-genus Gromov-Witten theory of one-parameter Calabi-Yau threefolds II: Feynman rule and anomaly equations Show more

   We prove the Feynman rule conjectured by Bershadsky-Cecotti-Ooguri-Vafa and the anomaly equations conjectured by Yamaguchi-Yau for the Gromov-Witten theory of the Calabi-Yau threefolds \(Z_6 \subset \mathbb{P}(1,1,1,1,2)\), \(Z_8 \subset \mathbb{P}(1,1,1,1,4)\), and \(Z_{10} \subset \mathbb{P}(1,1,1,2,5)\). These determine the generating series \(F_g\) of genus \(g\) Gromov-Witten invariants recursively from the lower-genus \( F_{h\lt g} \) up to \(3g−3\) unknown parameters.

2. Higher-genus Gromov-Witten theory of one-parameter Calabi-Yau threefolds I: Polynomiality Show more

   We prove a finite generation conjecture of Yamaguchi-Yau for the Gromov-Witten theory of the Calabi-Yau threefolds \(Z_6 \subset \mathbb{P}(1,1,1,1,2)\), \(Z_8 \subset \mathbb{P}(1,1,1,1,4)\), and \(Z_{10} \subset \mathbb{P}(1,1,1,2,5)\). In addition, a formula is given for the genus one Gromov-Witten potentials of these targets.

3. MSP theory for smooth Calabi-Yau threefolds in weighted \(\mathbb{P}^4\) Show more

   We develop the theory of Mixed-Spin-P fields for the three smooth Calabi-Yau threefold hypersurfaces in weighted projective space.

Invited talks

• Zhejiang University, Institute for Advanced Study in Mathematics Online geometry and physics seminar, December 2024. Video
• Yale University Geometry, symmetry, and physics seminar, November 2024
• Columbia University Enumerative geometry seminar, October 2024
• University of Illinois Urbana Champaign Algebraic geometry seminar, September 2024