**Ernesto Lupercio**

In this talk I will survey my recent work with Bernardo Uribe and Mainak Poddar on localization principles in Orbifold theories. First I will describe how the basic localization principle for the loop groupoid serves to establish a relationship between what we call the Cyclic Homology of an orbifold and its K-theory. Then I will explain how motivated by quantum field theory we can use the same principle to prove a localization formula for the orbifold motivic integral, and then imply the positive solution to a conjecture in birational geometry due to Ruan.

Matthew 2003-04-12