Past Kinderseminar

23 November 2011
11:30
Alejandra Garrido Angulo
Abstract
It is known that the minimum number of generators d(G^n) of the n-th direct power G^n of a non-trivial finite group G tends to infinity with n. This prompts the question: in which ways can the sequence {d(G^n)} tend to infinity? This question was first asked by Wiegold who almost completely answered it for finitely generated groups during the 70's. The question can then be generalised to any algebraic structure and this is still an open problem currently being researched. I will talk about some of the results obtained so far and will try to explain some of the methods used to obtain them, both for groups and for the more general algebraic structure setting.
2 November 2011
11:30
Alessandro Sisto
Abstract
<p>We will start off with a crash course in General relativity, and then&nbsp;I'll describe a 'recipe' for a time machine. This will lead us to the&nbsp;question whether or not the topology of the universe can change. We will&nbsp;see that, in some sense, this is topologically allowed. However, the&nbsp;Einstein equation gives a certain condition on the Ricci tensor (which&nbsp;is violated by certain quantum effects) and meeting this condition is a&nbsp;more delicate problem.</p>
26 October 2011
11:30
Martin Palmer
Abstract

I will begin by defining the notion of a characteristic class of surface bundles, and constructing the MMM (Miller-Morita-Mumford) classes as examples. I will then talk about a recent theorem of Church, Farb, and Thibault which shows that the characteristic numbers associated to certain MMM-classes do not depend on how the total space is fibred as a surface bundle - they depend only on the topology of the total space itself. In particular they don't even depend on the genus of the fibre. Hence there are many 'coincidences' between the characteristic numbers of very different-looking surface bundles.

A corollary of this is an obstruction to low-genus fiberings: given a smooth manifold E, the non-vanishing of a certain invariant of E implies that any surface bundle with E as its total space must have a fibre with genus greater than a certain lower bound.

Also, following the paper of Church-Farb-Thibault, I will sketch how to construct examples of 4-manifolds which fibre in two distinct ways as a surface bundle over another surface, thus giving concrete examples to which the theorem applies.

1 June 2011
11:30
Elisabeth Fink
Abstract
The talk will start with the definition of amenable groups. I will discuss various properties and interesting facts about them. Those will be underlined with representative examples. Based on this I will give the definition and some basic properties of sofic groups, which only emerged quite recently. Those groups are particularly interesting as it is not know whether every group is sofic.

Pages