Log Pseudoholomorphic Curves and Degeneration Formula (Current Project)

  • Towards a degeneration formula for the Gromov-Witten invariants of symplectic manifolds
    submitted, arXiv:1710.00599

  • Pseudoholomorphic curves relative to normal crossings symplectic divisors: compactification
    submitted, arXiv:1710.00224

Foundations of Gromov-Witten Theory

Normal Crossings Symplectic Divisors and Varieties

  • (with M. McLean and A. Zinger) Normal crossings singularities for symplectic topology; structures
    in preparation

  • (with M. McLean and A. Zinger) Normal crossings singularities for symplectic topology II
    in preparation

  • (with M. McLean and A. Zinger) Singularities and semistable degenerations for symplectic topology
    to appear in Comptes Rendus Mathematique (2018) (arXiv:1707.01464)

  • (with A. Zinger) Normal crossings degenerations of symplectic manifolds
    submitted, arXiv:1603.07661

  • (with M. McLean and A. Zinger) The smoothability of normal crossings symplectic varieties
    submitted, arXiv:1410.2573

  • (with M. McLean and A. Zinger) Normal crossings singularities for symplectic topology
    submitted, arXiv:1410.0609

Symplectic Sum Formula

  • (with A. Zinger) On the refined symplectic sum formula for Gromov-Witten invariants
    submitted, arXiv:1412.8205

  • (with A. Zinger) On the Rim tori refinement of relative Gromov-Witten invariants
    submitted, arXiv:1412.8204

  • (with A. Zinger) On symplectic sum formulas in Gromov-Witten theory
    Expository article, arXiv:1404.1898

Applications of Algebraic Geometry to Information Theory

Real/Open Gromov-Witten Theory

Other Subjects

Recorded Talks

On the compactification problem for (certain) moduli spaces of J-holomorphic maps, SCGP Fall 2017
Absolute vs. Relative GW invariants, IAS Fall 2015
Symplectic sum formulas: an overview, SCGP Winter 2014
Real Gromov-Witten theory in genus zero and beyond, SCGP Spring 2013

Slides

On Moduli Spaces of J-holomorphic Curves in Symplectic Manifolds, U Iowa, 2018
Symplectic normal crossings (sub-)varieties and their smoothings, Aarhus, Denmark, 2017

Misc

Lectures on Kuranishi structures by K. Fukaya; Spring 2014, Simons Center
Workshop on Moduli Spaces of Pseudo-holomorphic Curves I; March 17-21, 2014, Simons Center
Workshop on Moduli Spaces of Pseudo-holomorphic Curves II; June 2-6, 2014, Simons Center