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We construct orientations on moduli spaces of pseudoholomorphic quilts with seam conditions in Lagrangian correspondences equipped with relative spin structures and determine the effect of various gluing operations on the orientations. We also investigate the behavior of the orientations under composition of Lagrangian correspondences.
We construct families of quilted surfaces parametrized by the multiplihedra, and define moduli spaces of pseudoholomorphic quilted disks using the theory of pseudoholomorphic quilts of Wehrheim and Woodward. We prove a gluing theorem for regular, iso
This survey article, in honor of G. Tians 60th birthday, is inspired by R. Pandharipandes 2002 note highlighting research directions central to Gromov-Witten theory in algebraic geometry and by G. Tians complex-geometric perspective on pseudoholomorp
In this paper, we use the canonical connection instead of Levi-Civita connection to study the smooth maps between almost Hermitian manifolds, especially, the pseudoholomorphic ones. By using the Bochner formulas, we obtian the $C^2$-estimate of canon
Let $X$ be a compact manifold, $D$ a real elliptic operator on $X$, $G$ a Lie group, $Pto X$ a principal $G$-bundle, and ${mathcal B}_P$ the infinite-dimensional moduli space of all connections $ abla_P$ on $P$ modulo gauge, as a topological stack. F
We study several natural instances of the geometric hitting set problem for input consisting of sets of line segments (and rays, lines) having a small number of distinct slopes. These problems model path monitoring (e.g., on road networks) using the