Some Questions in the Theory of Pseudoholomorphic Curves

TL;DR

This survey discusses key questions and developments in the theory of pseudoholomorphic curves, emphasizing their role in Gromov-Witten theory and symplectic topology, inspired by G. Tian's work.

Contribution

It provides an overview of central research questions and recent progress in pseudoholomorphic curves within symplectic geometry.

Findings

Highlights the importance of pseudoholomorphic curves in Gromov-Witten theory

Connects complex geometry perspectives to symplectic topology advances

Identifies open questions guiding future research

Abstract

This survey article, in honor of G. Tian's 60th birthday, is inspired by R. Pandharipande's 2002 note highlighting research directions central to Gromov-Witten theory in algebraic geometry and by G. Tian's complex-geometric perspective on pseudoholomorphic curves that lies behind many important developments in symplectic topology since the early 1990s.