Moduli, Motives and Bundles : New Trends in Algebraic Geometry

This volume explores new developments in algebraic geometry and its interactions with number theory and mathematical physics, from the theory of moduli to motives and enumerative geometry. Covering a wide range of techniques, it is accessible to postgraduate students and young researchers, and researchers in adjacent fields of algebraic geometry.

The present volume features contributions from the 2022 BIRS-CMO workshop 'Moduli, Motives and Bundles – New Trends in Algebraic Geometry' held at the Casa Matemática Oaxaca (CMO), in partnership with the Banff International Research Station for Mathematical Innovation and Discovery (BIRS). The first part presents overview articles on enumerative geometry, moduli stacks of coherent sheaves, and torsors in complex geometry, inspired by related mini course lecture series of the workshop. The second part features invited contributions by experts on a diverse range of recent developments in algebraic geometry, and its interactions with number theory and mathematical physics, offering fresh insights into this active area. Students and young researchers will appreciate this text's accessible approach, as well as its focus on future research directions and open problems.