Past Seminars › Seminar Series

Algebra Seminar (past)

Tue, 12/06/2012
17:00 		Professor G. Clif (Alberta) Algebra Seminar Add to calendar L2
"PBW Bases for Representations of Lie Algebras".
Tue, 05/06/2012
17:00 		Professor S. Rees (Newcastle) Algebra Seminar Add to calendar L2
Artin groups of large type: from geodesics to Baum-Connes
I’ll report on my recent work (with co-authors Holt and Ciobanu) on Artin groups of large type, that is groups with presentations of the form G = hx1, . . . , xn | xixjxi · · · = xjxixj · · · , 8i < ji for which both sides of the ‘braid relation’ on xi and xj have length mij 2 N [1 with mij  3. (In fact, our results still hold when some, but not all possible, relations with mij = 2 are allowed.) Recently, Holt and I characterised the geodesic words in these groups, and described an effective method to reduce any word to geodesic form. That proves the groups shortlex automatic and gives an effective (at worst quadratic) solution to the word problem. Using this characterisation of geodesics, Holt, Ciobanu and I can derive the rapid decay property for most large type groups, and hence deduce for most of these that the Baum-Connes conjec- ture holds; this has various consequence, in particular that the Kadison- Kaplansky conjecture holds for these groups, i.e. that the group ring CG contains no non-trivial idempotents. 1
Tue, 22/05/2012
17:00 		Dr. M. de Visscher (City) Algebra Seminar Add to calendar L2
On simple modules for the Brauer algebra
Tue, 15/05/2012
17:00 		Aner Shalev (Jerusalem) Algebra Seminar Add to calendar L2
'More words on words'
In recent years there has been extensive interest in word maps on groups, and various results were obtained, with emphasis on simple groups. We shall focus on some new results on word maps for more general families of finite and infinite groups.
Tue, 08/05/2012
17:00 		Professor G. A. Jones (Southampton) Algebra Seminar Add to calendar L2
Groups and Beauville surfaces
Tue, 01/05/2012
17:00 		Professor R. Marsh (Leeds) Algebra Seminar Add to calendar L2
Reflection group presentations arising from cluster algebras

 Finite reflection groups are often presented as Coxeter groups. We give a
presentation of finite crystallographic reflection group in terms of an
arbitrary seed in the corresponding cluster algebra of finite type for which
the Coxeter presentation is a special case. We interpret the presentation in
terms of companion bases in the associated root system. This is joint work with 
Michael Barot (UNAM, Mexico)
Tue, 24/04/2012
17:00 		Professor M. Dunwoody (Southampton) Algebra Seminar Add to calendar L2
Groups acting on R-trees
Tue, 06/03/2012
17:00 		Dr Kobi Kremnitzer (Oxford) Algebra Seminar Add to calendar L2
Type theories and algebraic theories.
By recent work of Voevodsky and others, type theories are now considered as a candidate for a homotopical foundations of mathematics. I will explain what are type theories using the language of (essentially) algebraic theories. This shows that type theories are in the same "family" of algebraic concepts such as groups and categories. I will also explain what is homotopic in (intensional) type theories.
Tue, 28/02/2012
17:00 		Ashot Minasyan (University of Southampton) Algebra Seminar Add to calendar L2
"Tits alternatives for graph products of groups".

 Graph products of groups naturally generalize direct and free products and have a rich subgroup structure. Basic examples of graph products are right angled Coxeter and Artin groups. I will discuss various forms of Tits Alternative for subgroups and
their stability under graph products. The talk will be based on a joint work with Yago Antolin Pichel.
Tue, 31/01/2012
17:00 		Professor Martin Bridson (Oxford) Algebra Seminar Add to calendar L2
"On the undecidability of profinite triviality"
In this talk I'll describe recent work with Henry Wilton (UCL) in which we prove that there does not exist an algorithm that can determine which finitely presented groups have a non-trivial finite quotient.
Tue, 24/01/2012
17:00 		Professor Peter Kropholler (Glasgow) Algebra Seminar Add to calendar L2
"Group presentations in which the relators weigh less than the generators"
Tue, 17/01/2012
17:00 		Professor S Gurevich (Wisconsin) Algebra Seminar Add to calendar L2
Representation Theoretic Patterns in Digital Signal Processing I: Computing the Matched Filter in Linear Time
In the digital radar problem we design a function (waveform) S(t) in the Hilbert space H=C(Z/p) of complex valued functions on Z/p={0,...,p-1}, the integers modulo a prime number p>>0. We transmit the function S(t) using the radar to the object that we want to detect. The wave S(t) hits the object, and is reflected back via the echo wave R(t) in H, which has the form R(t) = exp{2πiωt/p}⋅S(t+τ) + W(t), where W(t) in H is a white noise, and τ,ω in ℤ/p, encode the distance from, and velocity of, the object. Problem (digital radar problem) Extract τ,ω from R and S. I first introduce the classical matched filter (MF) algorithm that suggests the 'traditional' way (using fast Fourier transform) to solve the digital radar problem in order of p^2⋅log(p) operations. I will then explain how to use techniques from group representation theory to design (construct) waveforms S(t) which enable us to introduce a fast matched filter (FMF) algorithm, that we call the "flag algorithm", which solves the digital radar problem in a much faster way of order of p⋅log(p) operations. I will demonstrate additional applications to mobile communication, and global positioning system (GPS). This is a joint work with A. Fish (Math, Madison), R. Hadani (Math, Austin), A. Sayeed (Electrical Engineering, Madison), and O. Schwartz (Electrical Engineering and Computer Science, Berkeley).
Tue, 29/11/2011
17:00 		Algebra Seminar Add to calendar L2
To Be Announced
Tue, 22/11/2011
17:00 		Prof L Scott (Virginia) Algebra Seminar Add to calendar L2
"Forced gradings and p-filtrations in algebraic group modules".
Tue, 15/11/2011
17:00 		J. Taylor (Aberdeen) Algebra Seminar Add to calendar L2
On Unipotent Supports for Finite Reductive Groups
Tue, 08/11/2011
17:00 		Dr Justin McInroy (Oxford) Algebra Seminar Add to calendar L2
"Biaffine geometries, amalgams and group recognition"
A polar space $ \Pi $ is a geometry whose elements are the totally isotropic subspaces of a vector space $ V $ with respect to either an alternating, Hermitian, or quadratic form. We may form a new geometry $ \Gamma $ by removing all elements contained in either a hyperplane $ F $ of $ \Pi $, or a hyperplane $ H $ of the dual $ \Pi^* $. This is a biaffine polar space. We will discuss two specific examples, one with automorphism group $ q^6:SU_3(q) $ and the other $ G_2(q) $. By considering the stabilisers of a maximal flag, we get an amalgam, or "glueing", of groups for each example. However, the two examples have "similar" amalgams - this leads to a group recognition result for their automorphism groups.
Tue, 01/11/2011
17:00 		Dr. N. Nikolov (Imperial) Algebra Seminar Add to calendar L2
Growth of Betti numbers in arithmetic groups
Tue, 01/11/2011
15:30 		Professor. J. Michel (Paris VII) Algebra Seminar Add to calendar SR2
The center of pure complex braid groups
Tue, 25/10/2011
17:00 		Dr. S. Goodwin (Birmingham) Algebra Seminar Add to calendar L2
Representations of finite W-algebras in classical type

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

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