Special Speakers

Sarah Yeakel (U Maryland)

When: 2016.10.04
Title: Derivatives in Goodwillie Calculus
Abstract: Goodwillie's calculus of functors is a method of approximating a homotopy functor with easier "polynomial" functors, building a Taylor tower where the homogeneous pieces are classified by certain spectra, called the derivatives of the functor. It is known that the derivatives of the identity functor of spaces form an operad and composable functors have a chain rule. We will discuss a general framework for these results and the extra structure that the derivatives possess. During the introductory talk, we will review the theory of functor calculus and why operads show up.

Laurentiu Maxim (U Wisconsin Madison)

When: 2016.10.18
Title: Alexander-Type Invariants of Complex Hypersurface Complements
Abstract: By analogy with knot theory, complex hypersurfaces can be studied via Alexander-type invariants of their complements. I will discuss old and new results concerning rigidity properties of such invariants, including (twisted) Alexander polynomials, L2-betti numbers and Novikov homology of hypersurface complements.

The first part of the talk will be an overview of the subject, addressed to a general audience. In the second part I will show how intersection homology and perverse sheaves can be used to relate the local and global topology of such hypersurface complements.

David Gepner (Purdue U)

When: 2016.11.01
Title: Cohomology Theories Associated to Elliptic Curves
Abstract: In this talk we will give a gentle introduction to chromatic homotopy theory with emphasis on the close connection between algebraic topology and algebraic geometry which arises from the theory of formal groups. We will then consider how this relationship can be made even closer by enlarging our scope to include spaces with group actions, and what this amounts to in the interesting case of elliptic cohomology.