The geometry, topology, and physics of moduli spaces of Higgs bundles

In the 25 years since their introduction, Higgs bundles have seen a surprising number of interactions within different areas of mathematics and physics. There is a recent surge of interest following Ng? Bau Chau's proof of the Fundamental Lemma and the work of Kapustin and Witten on the Geometric Langlands program. The program on The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles, was held at the Institute for Mathematical Sciences at the National University of Singapore during 2014. It hosted a number of lectures on recent topics of importance related to Higgs bundles, and it is the purpose of this volume to collect these lectures in a form accessible to graduate students and young researchers interested in learning more about this field. Readership: Graduate students and researchers interested in Higgs bundles and their interactions within different areas of mathematics and physics. "In the 25 years since their introduction, Higgs bundles have seen a surprising number of interactions within different areas of mathematics and physics. There is a recent surge of interest following Ngô Bau Châu's proof of the Fundamental Lemma and the work of Kapustin and Witten on the Geometric Langlands program. The program on The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles, was held at the Institute for Mathematical Sciences at the National University of Singapore during 2014. It hosted a number of lectures on recent topics of importance related to Higgs bundles, and it is the purpose of this volume to collect these lectures in a form accessible to graduate students and young researchers interested in learning more about this field."--Publisher's website Preface -- An introduction to the dierential geometry of flat bundles and of Higgs bundles / Olivier Guichard -- An introduction to spectral data for Higgs bundles / Laura P. Schaposnik -- Lectures on the topological recursion for hHggs bundles and quantum curves / Olivia Dumitrescu and Motohico Mulase -- An introduction to moduli stacks, with a view towards Higgs bundles on algebraic curves / Sebastian Casalaina-Martin and Jonathan Wise