Elliptic cohomology theories
Abstract
Using the theory of formal groups, Landweber´s exactness theorem provides means to construct interesting invariants of topological spaces out of geometric objects. I will illustrate the resulting connection between algebraic geometry and stable homotopy theory in the special case of elliptic curves.
Introduction to Golod-Shafarevich groups
Abstract
I will describe in detail the first construction of infinite, finitely generated torsion groups due to Golod in early 60s --
these groups are special cases of the so-called Golod-Shafarevich groups. If time allows, I will discuss some related constructions and open problems.
Presheaves on 2-categories
Abstract
Presheaves on categories crop up everywhere! In this talk, I'll give a
gentle introduction to 2-categories, and discuss the notion of a
presheaf on a 2-category. In particular, we'll consider which
2-categories such a presheaf might take values in. Only a little
familiarity with the notion of a category will be assumed!