Forthcoming Seminars › Seminar Series

Algebra Kinderseminar

Wed, 12/10/2011
11:30 		Owen Cotton-Barratt (University of Oxford) Algebra Kinderseminar Add to calendar
The Proof of the Hanna Neumann Conjecture (St Hugh's, 80 WR, 18)
The Hanna Neumann Conjecture provides a bound on the rank of the intersection of finitely generated subgroups of a free group. We will follow Mineyev's recent elementary and beautiful proof of this longstanding conjecture.
Wed, 26/10/2011
11:30 		Martin Palmer Algebra Kinderseminar Add to calendar
Coincidences between characteristic classes of surface bundles (St Hugh's, 80WR18)

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.
Wed, 02/11/2011
11:30 		Alessandro Sisto (University College, Oxford) Algebra Kinderseminar Add to calendar
General relativity+cobordism= time machine (maybe) (St Hugh's, 80WR18)
We will start off with a crash course in General relativity, and then I'll describe a 'recipe' for a time machine. This will lead us to the question whether or not the topology of the universe can change. We will see that, in some sense, this is topologically allowed. However, the Einstein equation gives a certain condition on the Ricci tensor (which is violated by certain quantum effects) and meeting this condition is a more delicate problem.
Wed, 09/11/2011
11:30 		David Hume Algebra Kinderseminar Add to calendar
Mathematical models of composition (St Hugh's, 80WR18)
We explore methods (deterministic and otherwise) of composing music using mathematical models. Musical examples will be provided throughout and the audience (with the speakers assistance) will compose a brand new piece.
Wed, 16/11/2011
11:30 		Peter Neumann Algebra Kinderseminar Add to calendar
Derangements (St Hugh's, 80WR18)
Wed, 23/11/2011
11:30 		Alejandra Garrido Angulo Algebra Kinderseminar Add to calendar
On $ d $-sequences (or, Growth of generating sets for direct powers of algebraic structures)
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.

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

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