GT Seminar with Tobias Ekholm (Uppsala university).

Abstract: In a series of talks we will discuss how to count bare holomorphic curves with Lagrangian boundary conditions in a Calabi-Yau 3-fold. Here bare means that the curves does not have any symplectic area zero components. The main application and motivation for this is the construction of invariant skein valued counts of open curves. In this first talk we will explain  why the usual approaches to Gromov-Witten counts does not work to define skein valued counts and present one of the key technical results for bare counts: we finds a class of perturbations for the Cauchy-Riemann equations that has the property that if a ghost bubbles forms in the limit of sequence of bare curves then it leaves a trace (e.g. vanishing complex derivative) on the limiting positive area curve on which it is attached. In later talks we will construct a perturbation scheme using polyfold language with perturbations of this kind that gives rise to solutions of the perturbed Cauchy-Riemann equations that admit forgetful maps. The talks report on joint work with Vivek Shende.

See upcoming seminars in our seminar series on Geometry and Topology (GT).