A _∞ Structures And Moduli Spaces

This textbook introduces exciting new developments and cutting-edge results on the theme of hyperbolicity. Written by leading experts in their respective fields, the chapters stem from mini-courses given alongside three workshops that took place in Montréal between 2018 and 2019.

This work presents the proceedings of a July 1998 workshop that was held to explain to nonspecialists the different uses of modulli spaces in various areas of mathematics and physics, such as differential and algebraic geometry, dynamical systems, Yang-Mills theory, and conformal field theory. Seven papers offer different perspectives on areas including Hodge theory and deformations of complex structures, moduli spaces of vector bundles on algebraic varieties, some uses of moduli spaces in particle and field theory, and the use of parameter and moduli spaces in curve counting.

The package of Gromov’s pseudo-holomorphic curves is a major tool in global symplectic geometry and its applications, including mirror symmetry and Hamiltonian dynamics. The Kuranishi structure was introduced by two of the authors of the present volume in the mid-1990s to apply this machinery on general symplectic manifolds without assuming any specific restrictions.