Groups in Galway 2009
The 2009 'Groups in Galway' conference takes place at the National
University of Ireland, Galway, on 79 May, 2009.
This year we are celebrating the opening of the
de Brun Centre for Computational Algebra here at NUI Galway
with a special afternoon on Computational Group Theory.
Groups in Galway has been running on an annual basis since 1978.
The scope of the conference covers all areas of group theory, applications,
and related fields. All who are interested are invited to attend. The webpage of last year's Groups in Galway conference is located here.
As in the last two years there will be a poster session and wine reception before the conference dinner on the evening of Friday May 8.
Speakers
Confirmed speakers at the moment include

Prof José Burillo (Universitat Politécnica de Catalunya)

Dr Inna (Korchagina) Capdeboscq (University of Warwick)

Hannah Coutts (University of St Andrews)

Dr Will Dison (University of Bristol)

Prof Bernard Hanzon (UCC)

Dr Aisling Kenny (DCU)

Dr Benjamin Klopsch (Royal Holloway)

Prof Tom Laffey (UCD)

Dr James Mitchell (University of St Andrews)

Dr Rachel Quinlan (NUI Galway)

Dr Michah Sageev (Technion, Israel)

Prof Leonard Soicher (Queen Mary)

Dr Richard Weidmann (University of Edinburgh)
Schedule
Below is a tentative schedule which may still change but only minimally. All talks will be in the Arts Millenium Building; on Thursday and Friday in AM250 and on Saturday in AM150.
Coffee breaks will be in C219 (Áras de Brún).
Move the cursor over a title for a short abstract, or try clicking for a PDF version of the full abstract.
Thursday 7 May
2.002.45
Leonard Soicher
The Joy of GAP Packages
GAP is a freely available opensource system for computation with
groups and related structures. The main GAP system is supplemented by
usercontributed packages, providing useful extensions to GAP, such as
interfaces to other mathematical software systems and standalone programs,
packages for research in certain specialised areas of group theory and
algebra, databases of groups and related objects, tools for graphics and
documentation, and extensions of GAP into areas making use of groups, such
as graph theory and coding theory. It is worth noting that significant
contributions of GAP packages have come from researchers at NUI Galway.
Central to the GAP package administration is a refereeing system,
whereby a package can obtain an official status of "accepted", so that
quality is maintained and package authors can obtain credit as they
would for a journal publication.
In this talk, I will give a brief overview of GAP packages and the package
refereeing system. I will discuss in more detail some of the mathematical,
computational and historical aspects of my GRAPE and DESIGN packages,
and present to you the many benefits of writing a GAP package.
2.453.30
Will Dison
Hugely distorted subgroups
I will be discussing some joint work with Tim Riley. For each natural
number n, we construct a pair of groups H < G which possess many nice
properties (G is CAT(0), freebycyclic, 1relator; H is finitely
generated free) but for which the distortion of H in G is huge 
specifically, the distortion function grows like the n^th Ackermann
function. In my talk I'll explain what these Ackermann functions are,
how they arise as the time functions of certain 'word games', and how we
encode these games into group presentations.
3.304.00
Coffee/tea
4.004.45
Hannah Coutts
Computing normalizers of matrix groups
The matrix group recognition project dates back to the early 1990s. This
international research project within computational group theory aims to
produce efficient algorithms for solving problems with matrix groups,
using systems Magma and GAP.
Let G < GL_n(q). The current method of computing the
normalizer N of G is to perform a backtrack
search on the elements of GL_n(q). This becomes unreasonably
timeconsuming rather quickly as the values of n and q increase. We use
Aschbacher's theorem to determine a geometric structure preserved by G
and construct an overgroup C > N by
considering the action of N on this
structure. Now the computation of the normalizer of G in C is often much faster
than that of N as the search space is
greatly reduced.
4.455.30
Bernard Hanzon
Financial mathematics, linear dynamical systems and orthogonal
transformation groups
Linear dynamical systems are used in many different areas of science in
the broad sense, including financial mathematics. Linear and affine
dynamical state space models are used for modeling interest rates.
Interest rates depend on the time to maturity and therefore at each
point in time one has a large number of different interest rates to deal
with. Mathematically this can be modeled using an infinite dimensional
state space model (such as the HeathJarrowMorton model). In practice,
however, the model can often be replaced (or approximated) by a finite
dimensional state space model.
One of the issues that arise when using (finite dimensional) linear
state space models is dealing with the indeterminacy that arises from
the choice of basis of the state space. Under certain conditions it can
be shown that the indeterminacy can be represented as the choice of an
element of the general linear group. In the literature various
normalizations are known including making the system "input normal" or
"output normal"; also one can require the partitioned matrix that
represents the system (the socalled realization matrix) to have minimal
Frobenius norm. There are a number of other normalizations as well
(going under such names of Grammian balanced, Riccatibalanced etc).
The normalizations that we are referring to here are such that the
remaining choice of basis of the state space reduces to a choice of an
element of the orthogonal group (or unitary group in the complex case)
instead of the general linear group.
We will present recent results on how the action of the orthogonal group
on a linear dynamical state space system can be used to bring the system
in a special form, called a subdiagonal pivot structure, which has a
number of nice properties: For instance it can be used to detect whether
an exact or approximate representation of the model is possible which
uses a lower dimensional state space.
Friday 8 May
10.0010.45
Tom Laffey
Solving matrix equations and Galois groups
Let A be an n by n matrix with rational entries and f(x) a polynomial
with rational coefficients for which the equation f(X)=A has a matrix solution X over the
complex numbers. We consider the minimal degree of a field extension F of the
rational numbers for which such a solution X can be found with entries in F.
The problem leads to questions on Galois groups. The particular case
f(x)=x^2
will be used to illustrate the discussion. Some polynomials with ''interesting''
Galois groups will be given. The presentation will include some results obtained jointly with Bryan Cain
and with Raja Mukherji.
11.0011.45
Richard Weidmann
Minimal generating sets of Coxeter groups
We show that the standard generating set of a Coxeter group is
minimal provided that all nondiagonal entries of the Coxeter matrix are
suffieciently large, this is joint work with Mathieu Carette.
11.4512.15
Coffee/tea
12.151.00
Rachel Quinlan
The Early Days of Character Theory
Characters of finite groups are well known as trace functions associated to
matrix representations. However the notion of character was extended from
abelian groups to general finite groups by Frobenius in 1896, without
explicit reference to their associated matrix representations. Motivated by
the problem of factorizing the group determinant as proposed to him by
Dedekind, Frobenius defined (irreducible complex) characters and established
many of their most important properties in an astonishingly short time
during
the spring of 1896. In this talk we will discuss some aspects of the
development of these ideas, as documented in the correspondence of Dedekind
and Frobenius.
1.002.30
Lunch
2.303.15
Michah Sageev
Quasiisometries and right angled Artin groups
Sorry, no abstract available.
3.154.00
Inna (Korchagina) Capdeboscq
Finite Simple Groups with double life
In this talk we will discuss classification of finite simple
groups
that belong to two distinct types (in the sense of the project of
Gorenstein, Lyons and Solomon
on the Classification of finite Simple Groups).
4.004.30
Coffee/tea
4.305.15
Benjamin Klopsch
Representation Growth
In a joint project with Christopher Voll, I have investigated the
representation zeta functions of compact padic Lie groups and
arithemtic groups.
In my talk I will start with an introduction to the subject. Then I
will explain
some of our results, e.g. the existence of functional equations in a
suitable global
setting, and I will discuss open problems.
In particular, I will indicate how piecing together information about
local zeta
functions allows us to determine the precise abscissae of convergence
for the
representation zeta functions of arithmetic subgroups of
SL_3(R),
e.g. SL_3(Z)
5.30
Poster Session and Wine Reception
7.30
Conference Dinner: Vina Mara, Middle Street
Saturday 9 May
10.0010.45
Aisling Kenny
Homology of noncrossing partition lattices
For any finite real reflection group W, we construct a geometric
basis for the homology of the noncrossing partition lattice. Then, using
a general construction of a generic affine hyperplane for the central
hyperplane arrangement defined by W, we relate this basis to the basis for
the homology of the corresponding intersection lattice.
10.4511.15
Coffee/tea
11.1512.00
James Mitchell
Generating the symmetric group and some related semigroups
Sorry, no abstract available.
12.151.00
José Burillo
Higher Dimensional Thompson Groups
Sorry, no abstract available.
Travel and Accommodation

Travel
There are regular rail
connections from Dublin to Galway, and
bus
connections from all Irish cities and towns.
There are direct flights to Galway Airport from Belfast,
Dublin, Luton, Manchester, Edinburgh, Liverpool, Lorient, Cardiff,
Leeds, Cork and Prague. The Airport is 7kms from the NUI Galway
campus. Taxis typically cost €25.
Directions to NUI Galway by road can be found
here
.
NUI Galway has a number of payanddisplay
parking places for visitors. Cars parked in other spaces on the NUI
Galway campus and not displaying a valid parking permit will be
clamped.

Accommodation: The following are convenient for the NUI Galway campus:
 The Westwood Hotel, 091 521 442
 Bologna B&B, 091523792
 Corrib Haven B&B, 091524171
 Aneesha B&B, 091524250
 Ashgrove House B&B, 091581291
 Villanova B&B, 091524849
 Coolavalla B&B, 091522415
 Rosgal B&B, 091 524723
 De Sota B&B, 091585064
Please contact Ireland West
for further information about accommodation near NUI Galway.
For further information, please keep an eye on this website which will be updated regularly, or contact one of the organizers, Javier Aramayona or Claas Röver.
Groups in Galway 2009 is generously supported by
 The Office of the Registrar and Deputy President, NUI Galway
 The Millennium Research Fund, NUI Galway
 De Brun Centre for Computational Algebra, NUI Galway
 School of Mathematics, Statistics and Applied Mathematics, NUI Galway