Research

Research interest: 

Symplectic topology, Fukaya category, mirror symmetry, low dimensional topology, Hamiltonian dynamics 

Publications and preprints:

Hameomorphism groups of positive genus surfaces. (with Ibrahim Trifa)

• Submitted

Coulomb branch algebras via symplectic cohomology (with Eduardo González and Dan Pomerleano)

• Submitted

A characterization of heaviness in terms of relative symplectic cohomology. (with Yuhan Sun and Umut Varolgunes)

• J. Topol. (2024), 17: e12327.

Some cute applications of Lagrangian cobordisms towards examples in quantitative symplectic geometry. (with Jeff Hicks)

• Submitted

Subleading asymptotics of link spectral invariants and homeomorphism groups of surfaces. (with Daniel Cristofaro-Gardiner, Vincent Humilière, Sobhan Seyfaddini and Ivan Smith)

• Submitted

Affine nil-Hecke algebras and Quantum cohomology. (with Eduardo González and Dan Pomerleano)

• Adv. Math. (2023), vol. 415

Quantitative Heegaard Floer cohomology and the Calabi invariant. (with Daniel Cristofaro-Gardiner, Vincent Humilière, Sobhan Seyfaddini and Ivan Smith)

•  Forum Math. Pi (2022), vol. 10, e27

Circular spherical divisors and their contact topology. (with Tian-Jun Li and Jie Min)

• to appear in Comm. Anal. Geom.

Non-displaceable Lagrangian links in four-manifolds. (with Ivan Smith)

• Geom. Funct. Anal. 31 (2021), no.2, 438-481

Fukaya-Seidel categories of Hilbert schemes and parabolic category O. (with Ivan Smith)

• J. Eur. Math. Soc. (2021)

Tropically constructed Lagrangians in mirror quintic threefolds. (with Helge Ruddat)

• Forum Math. Sigma. (2020), vol. 8, e58 

Dehn twists and Lagrangian spherical manifolds. (with Weiwei Wu)

• Selecta Math.  25 (2019), article no. 68 

Symplectic divisorial capping in dimension 4. (with Tian-Jun Li)

• J. Symplectic Geom. 17 (2019), no. 6, 1835-1852

Dehn twists exact sequences through Lagrangian cobordism. (with Weiwei Wu)

• Compos. Math. 154 (2018), no. 12, 2485–2533

The Kodaira dimension of contact 3-manifolds and geography of symplectic fillings. (with Tian-Jun Li)

• Int. Math. Res. Not. (2018), rny166

Geometry of symplectic log Calabi-Yau pairs. (with Tian-Jun Li)

• ICCM Not. 6 (2018), no. 2, 42 – 50

Calabi-Yau caps, Uniruled caps and symplectic fillings. (with Tian-Jun Li and Kouichi Yasui)

• Proc. Lond. Math. Soc. (3) 114 (2017), no. 1, 159 - 187

Symplectic log Calabi-Yau surface - deformation class. (with Tian-Jun Li)

• Adv. Theor. Math. Phys. 20 (2016), no. 2, 351 - 379

Multifractal spectrum of self-similar measures with overlap. (with Cameron Bruggeman and Kathryn Hare)

• Nonlinearity 27 (2014), no. 2, 227 - 256.