# Past Kinderseminar

28 October 2009
11:30
Owen Cotton-Barratt
Abstract
Much of group theory is concerned with whether one property entails another. When such a question is answered in the negative it is often via a pathological example. We will examine the Rips construction, an important tool for producing such pathologies, and touch upon a recent refinement of the construction and some applications. In the course of this we will introduce and consider the profinite topology on a group, various separability conditions, and decidability questions in groups.
• Kinderseminar
21 October 2009
11:30
Peter Pappas
Abstract
The semisimplicity problem is the long-standing conjecture that the group algebra $KG$ of a $p'$-group $G$ over a field $K$ of characteristic $p\geqslant 0$ has zero Jacobson radical. We will discuss recent advances in connection with this problem.
• Kinderseminar
14 October 2009
11:30
Abstract
• Kinderseminar
17 June 2009
11:30
Mikhail Ershov
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.
• Kinderseminar
10 June 2009
11:30
Tobias Barthel
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.
• Kinderseminar
27 May 2009
11:30
Abstract
• Kinderseminar
20 May 2009
11:30
David Craven
Abstract
We begin by proving the abc theorem for polynomial rings and looking at a couple of its consequences. We then move on to the abc conjecture and its equivalence with the generalized Szpiro conjecture, via Frey polynomials. We look at a couple of consequences of the abc conjecture, and finally consider function fields, where we introduce the abc theorem in that case.
• Kinderseminar