Publication 1: Worldsheet Instantons and Torsion Curves, Part B: Mirror Symmetry. (URL) Publication 2: Partition Functions, Localization, and the Chiral de Rham complex. (URL) Publication 3: Resolved Toroidal Orbifolds and their Orientifolds. (URL) URL of Research: Statement of Interest:
Various aspects of topological strings on Calabi-Yau manifolds such as the computation of Gopakumar-Vafa invariants and non-perturbative contributions to the N=1 superpotential in 4D gauge theories. A different aspect is the interplay between geometry and conformal field theory descriptions of these theories and in particular their D- branes, using e.g. matrix factorizations. This aspect leads beyond the topological limit and allows the study the massive modes using chiral CFTs on Calabi-Yau manifolds. The relevant framework is the so-called chiral de Rham complex which is related to heterotic (0,2) compactifications.