Groups in Galway has been running on an annual basis since 1978. The scope of the conference workshop covers all areas of group theory, applications, and related fields. All who are interested are invited to attend. There is no conference fee. The webpage of last year's Groups in Galway conference workshop is located here.
10.00-10.45 Philippe Elbaz-Vincent The group K_8(Z) is trivial
On the homology of linear groups over imaginary quadratic fields
Abstract: Let Gamma be the group GL_N (OO_D), where OO_D is the ring of integers in the imaginary quadratic field with negative discriminant D. In this talk, we discuss the cohomology of Gamma for N=3,4 and for a selection of discriminants: D greater than or equal to -24 when N=3, and D=-3,-4 when N=4. In particular we compute the integral cohomology of Gamma up to p-power torsion for small primes p. Our main tool is the polyhedral reduction theory for Gamma developed by Ash and Koecher. Our results extend work of Staffeldt, who treated the case n=3, D=-4. In future work, we will apply some of these results to the computations with the K-groups K_4 (OO_D), when D=-3,-4.
This is joint work with Paul E. Gunnells, Jonathan Hanke, Achill Schuermann, Mathieu Dutour Sikiric and Dan Yasaki.
A Brief History of Moonshine
Abstract: It is 35 years since original Conway and Norton published their Monstrous Moonshine Conjectures. In this talk I will review some of the many subsequent related discoveries in the area of vertex operator algebras and conformal field theory.
A characterisation of nilpotent blocks
Abstract: The broader context for this talk is the interplay between the structure theory of finite groups and their p-local structure. The notion of p-local structure has been axiomatised by Puig in the early 1990s, leading to abstract fusion systems. These have been studied by many authors in the last decade, motivated by applications in homotopy theory and modular representation theory. The general theory of fusion systems starts feeding back into modular representation theory. The present talk describes a result in this spirit, generalising a character theoretic result of Isaacs to block algebras. This is joint work with R. Kessar and G. Navarro.
4.00-4.45 Radha Kessar On transitive block fusion systems
5.00 Poster Competition and Reception with refreshments in ADB1020 (Mathematics seminar room) in Áras de Brún
7.30 Conference workshop dinner : Vina Mara, Middle Street, 3 courses, 24 Euro, speakers funded.
Hilbert's Third Problem and Scissors Congruence Groups
Abstract: Hilbert's third problem was to find two polyhedra of equal volume neither of which can be subdivided into finitely many pieces and re-assembled to equal the other (we say they are `scissors-congruent' if this can be done). It was solved in 1900 by Max Dehn, who introduced a new invariant of (scissors-congruence classes of) polyhedra for the purpose. Much later, in 1965, J. P. Sydler showed that volume and Dehn invariant are a complete set of invariants for classes of polyhedra in 3-dimensional Euclidean space. However, the corresponding problems for hyperbolic and spherical space have been much studied in the last thirty years because of their connections with K-theory, motivic cohomology, regulators and polylogarithms, homology of Linear groups and several other topics of current interest. I will give an overview of the history of these questions and discuss some recent related developments.
Systoles and Dehn surgery for hyperbolic 3-manifolds
Abstract: Let G < PSL(2,C) be a finite covolume Kleinian group, and let M = H^3/G. The systole of M is its shortest closed geodesic, and the systole length can be studied via traces of elements of G. In this talk, I'll discuss the relationship between systole length and volume in M, and prove an asymptotic upper bound for systole length in terms of volume when G is non-cocompact. This result is applied to show that given any 3-manifold M and any knot or link L in M, although the volume of the complement M-L is unbounded, the systole length is bounded independent of L. This is joint work with Chris Leininger.
From finite sets to group algebras
Abstract: Let X be a finite set. In a joint work with Serge Bouc, we construct a finite-dimensional algebra canonically associated to X and we study its structure. We consider the algebra of the monoid of all relations on X, modulo the ideal generated by the relations factorizing through a set of cardinality strictly smaller than Card(X), called inessential relations. This quotient is called the essential algebra associated to X. We then define a suitable nilpotent ideal of the essential algebra and describe completely the structure of the corresponding quotient, a product of matrix algebras over suitable group algebras. In particular, we obtain a description of all the simple modules for the essential algebra.
There are regular rail
connections from Dublin to Galway, and
connections from all Irish cities and towns.
From Great Britain, Galway can be reached by Sail and Rail. If you have a longer journey than from the British Isles, then Dublin Airport and Shannon Airport will probably be the most convenient places to land in Ireland. From Dublin airport there are direct shuttle buses to Galway operated by Citylink and GoBus.
There are flights to Shannon Airport from Birmingham, Edinburgh, Heathrow, London City and Manchester by Aer Lingus.
Galway Airport is out of passenger operation.
Directions to NUI Galway by road can be found here .
Galway is a small city and you can reach any destination in the city center comfortably by walking. It takes about 15 minutes from Galway Coach Station to the university (Google maps direction).
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.
Please contact Ireland West for further information about accommodation near NUI Galway.
Groups in Galway 2014 is generously supported by