In this introductory lecture, which should be accessible to a general mathematical audience, I will review the classical bordism theory of manifolds, from its origin in Poincare's work, to the subsequent development by Pontryagin, Thom, Milnor, Wall, and Quillen among others.
Lecture 2: Bordism of orbifolds
An orbifold is a space with additional structure that describes it locally as the quotient of a manifold by a finite group. I will describe Pardon's recent result which reduces the study of orbifolds to the study of manifolds with Lie group actions. Then I will explain the relationship between equivariant and orbifold bordism, and formulation some structural properties of this theory.
Lecture 3: Bordism of derived orbifolds
The notion of a derived orbifold arises naturally in pseudo-holomorphic curve theory, and plays a central role in the emerging field of Floer homotopy. I will explain how it is related to the notion of "homotopical bordism" due to tom Dieck in the 1970s, and formulate some conjectures about its structure in the complex oriented case.
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