Abstracts for Geometry and Topology Seminar

In homotopy theory the existence of spectrum level ring structures
is an important question for theoretical and computations purposes.
We discuss the existence and uniqueness of these ring structure 
on algebraic and topological K-theory. Instead of using the 
classical approach with carefully chosen 'infinite loopspace 
machines' or obstruction theory our main tool will be the use 
of certain universal properties. This has the advantage of 
giving strong uniqueness results and also works in parametrized 
situations.

Three classic topics in discrete geometry are the ham sandwich
theorem, the center point theorem, and Tverberg's theorem.
This talk is about a common generalization, which lives in projective space.

This is joint work with Roman Karasev.

We introduce a complex that encodes isotopy classes of curves
representing a primitive homology class.
The complex, called the Kakimizu complex of a surface, is inspired by its 3-dimensional analogue, the Kakimizu complex of a 3-manifold.  We will discuss its relation to the cyclic cycle complex defined by A. Hatcher and the homology curve complex defined by I. Irmer.  Several results on the Kakimizu complex of a 3-manifold carry over to the setting of the Kakimizu complex of a surface.

Manifold calculus of functors is a machinery invented by Goodwillie and Weiss in order to study spaces of smooth embeddings of one manifold into another. I will briefly recall this construction as well as the connection to operads. For a particular example of the space of long embeddings R^m in R^n, n>2m+1, this connections describes the rational homology and
homotopy as the homology of very explicit graph-complexes similar to those introduced by Kontsevich.