Speaker: Chiu-Chu Melissa Liu

Title: Virtual fundamental classes in algebraic geometry

Abstract: A Deligne-Mumford stack is virtually smooth if it is equipped with a perfect obstruction theory--in particular, it has a virtual tangent bundle which is locally the difference of two vector bundles. Li-Tian and Behrend-Fantechi constructed virtual fundamental classes on virtually smooth Deligne-Mumford stacks. This is an expository talk on Behrend and Fantechi's construction.