Preface

There has been mutually stimulating interaction between geometry and physics since the days of Euclid (300 BC), and more recently, of Newton, Maxwell and Einstein. In the past 30 years, even  more exciting interactions between geometry and physics have emerged through  the work of Donaldson in applying gauge theory to low dimensional topology,  Witten's quantum field theory interpretations of Jones/Donaldson polynomials, Fukaya-Ono/Ruan-Tian's mathematical work on Gromov-Witten theory, and more recently through Kapustin-Witten's work on electric-magnetic Duality and its relation to the geometric Langlands program.  These introductory lecture series and the subsequent international conference will bring together international leaders  in these areas to foster communication and to initiate collaboration in Australia. 

There are three mini-courses in the first part of the event. The topics covering virtual techniques for moduli spaces by Bohui Chen, Floer instanton homology for 3-manifolds with boundary by Kenji Fukaya, and Symplectic Floer homology and its applications by Kaoru Ono.  There are 19 conference talks covering a wide range of topics in  Gromov-Witten theory, Gauge Theory and Dualities. 

• Prof. Bohui Chen (Sichuan University, China): Equivariant Donaldson Theory;

• Prof. Cheol-Hyun Cho (Seoul National University, South Korea): Non-commutative homological mirror functor;

• Prof. Huijun Fan (Beijing University, China): Analytic theory of Gauged Linear Sigma Model;

• Prof. Bohan Fang (Beijing University, China): Global mirror curve of a toric Calabi-Yau 3-fold;

• Prof. Kenji Fukaya (Simons Centre for Geometry and Physics, Stony Brook): Lagrangian Correspondence and A∞ functor;

• Prof. Andriy Haydys (University of Bielefeld, Germany): A compactness theorem for the Seiberg-Witten equations with multiple spinors;

• Prof. Pedram Hekmati (IMPA, Rio de Janeiro, Brazil): Gauge theoretic moduli spaces on foliated 5-manifolds;

• Prof. Jianxun Hu (Zhongshan University, China): The Gromov-Witten invariants of the Hilbert schemes of points on surfaces with pg > 0;

• Prof. Hiroshi Iritani (Kyoto University, Japan): Shift operators and toric mirror symmetry;

• Prof. Bumsig Kim (KIAS, Seoul, South Korea): Mirror Theorem for Elliptic Quasimap Invariants;

• Prof. Xiaobo Liu (Beijing University, China): Genus-2 generating functions for semisimple cohomological field theory;

• Prof. Ziming Ma (National Taiwan University): Scattering in the SYZ prohramme;

• Prof. Alina Marian (Northeastern University, USA): Segre classes and tautological rela-tions on the moduli space of polarized K3 surfaces;

• Prof. Daniel Mathews (Monash University, Australia): Trinities, sutured Floer homology, and contact structures;

• Prof. Yong-Geun Oh (IBS, South Korea): Bulk deformations and nondisplaceable La-grangian tori;

• Prof. Hiroshi Ohta (Nagoya University, Japan): Lagrangian Floer theory and categorical Saito theory;

• Prof. Kauro Ono (Kyoto University, Japan): spectral invariants in symplectic topology;

• Prof. Brett Parker (Australian National University, Australia): Tropical gluing formula for Gromov-Witten invariants; item Prof. Siye Wu (National Tsing-Hua University):Non-orientable surfaces and electric-magnetic duality.

This volume contains the proceedings of the conference. Each article in this volume was peer refereed. We thank all the authors for the contributions, and referees to their attention to detail.