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Algebra Kinderseminar (past)

Wed, 18/01/2012
11:30 		Peter Pappas (Oxford) Algebra Kinderseminar Add to calendar
On the Unit Conjecture for Group Rings – St Hugh's 80WR18
I will present a history of the problem, relate it to other conjectures, and, with time permitting, indicate recent developments. The focus will primarily be group-theoretic and intended for the non-specialist.
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.
Wed, 16/11/2011
11:30 		Peter Neumann Algebra Kinderseminar Add to calendar
Derangements (St Hugh's, 80WR18)
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, 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, 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, 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, 22/06/2011
11:30 		David Craven (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
Things I haven't managed to do
This talk will summarize some of the problems and conjectures that I haven't managed to solve (although I have tried to) while spending my three years in this job. It will cover the areas of group theory, representation theory, both of general finite groups and of symmetric groups, and fusion systems.
Wed, 01/06/2011
11:30 		Elisabeth Fink (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
Sophic groups
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.
Wed, 25/05/2011
11:30 		Chris Gill (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
On the Brauer construction and p-Kostka numbers
Wed, 18/05/2011
11:30 		Algebra Kinderseminar Add to calendar
NO SEMINAR
Wed, 11/05/2011
11:30 		Jan Grabowski (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
The hitchhiker's guide to quantum algebra
Wed, 04/05/2011
11:30 		David Stewart (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
Unbounding Ext
Wed, 09/03/2011
11:30 		Chloé Perin (Strasbourg) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
The first-order logic of free groups
The long-open Tarski problem asked whether first-order logic can distinguish between free groups of different ranks. This was finally answered in the negative by the works of Sela and Kharlampovich-Myasnikov, which sparked renewed interest in the model theoretic properties of free groups. I will give a survey of known results and open questions on this topic.
Wed, 02/03/2011
11:30 		Algebra Kinderseminar Add to calendar
No Seminar
Wed, 23/02/2011
11:30 		David Craven (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
Weight 2 blocks of symmetric groups
The representation theory of the symmetric groups is far more advanced than that of arbitrary finite groups. The blocks of symmetric groups with defect group of order pn are classified, in the sense that there is a finite list of possible Morita equivalence types of blocks, and it is relatively straightforward to write down a representative from each class.In this talk we will look at the case where n=2. Here the theory is fairly well understood. After introducing combinatorial wizardry such as cores, the abacus, and Scopes moves, we will see a new result, namely that the simple modules for any p-block of weight 2 "come from" (technically, have isomorphic sources to) simple modules for S2p or the wreath product of Sp and C2.
Wed, 16/02/2011
11:30 		Matt Towers (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
Non-standard analysis
I will give a short introduction to non-standard analysis using Nelson's Internal Set Theory, and attempt to give some interesting examples of what can be done in NSA. If time permits I will look at building models for IST inside the usual ZFC set theory using ultrapowers.

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

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