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.
2.00-2.45 Leonard Soicher The Joy of GAP Packages GAP is a freely available open-source system for computation with groups and related structures. The main GAP system is supplemented by user-contributed 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.
2.45-3.30 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), free-by-cyclic, 1-relator; 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.
4.00-4.45 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 time-consuming 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.
4.45-5.30 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 Heath-Jarrow-Morton 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 so-called realization matrix) to have minimal Frobenius norm. There are a number of other normalizations as well (going under such names of Grammian balanced, Riccati-balanced 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 sub-diagonal 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.
10.00-10.45 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.
11.00-11.45 Richard Weidmann Minimal generating sets of Coxeter groups We show that the standard generating set of a Coxeter group is minimal provided that all non-diagonal entries of the Coxeter matrix are suffieciently large, this is joint work with Mathieu Carette.
12.15-1.00 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.
2.30-3.15 Michah Sageev Quasi-isometries and right angled Artin groups Sorry, no abstract available.
3.15-4.00 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).
4.30-5.15 Benjamin Klopsch Representation Growth In a joint project with Christopher Voll, I have investigated the representation zeta functions of compact p-adic 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
10.00-10.45 Aisling Kenny Homology of non-crossing partition lattices For any finite real reflection group W, we construct a geometric basis for the homology of the non-crossing 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.
11.15-12.00 James Mitchell Generating the symmetric group and some related semigroups Sorry, no abstract available.
12.15-1.00 José Burillo Higher Dimensional Thompson Groups Sorry, no abstract available.
There are regular rail
connections from Dublin to Galway, and
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 pay-and-display parking places for visitors. Cars parked in other spaces on the NUI Galway campus and not displaying a valid parking permit will be clamped.
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