Groups in Galway 2013

10-11 May, 2013

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. There is no conference fee. The webpage of last year's Groups in Galway conference is located here.

Speakers

Confirmed speakers at the moment include

Schedule

Below is a tentative schedule which may still change but only minimally. All talks will be in AC201 in the Concourse.

Move the cursor over a title for a short abstract.

Friday 10 May

10.00-10.45 Brita Nucinkis Bredon cohomological finiteness conditions for generalisations of Thompson groups We define a family of groups that generalises Thompson's groups T and G, and also those of Higman, Stein and Brin. For groups in this family we describe centralisers of finite subgroups and show, that for a given finite subgroup Q, there are finitely many conjugacy classes of finite subgroups isomorphic to Q. We use this to show that our groups have a slightly weaker property, quasi-F∞, to that of a group possessing a finite type model for the classifying space for proper actions EG if and only if they admit finite type models for the ordinary classifying space (joint work with C. Martínez-Pérez and Francesco Matucci).

10.45-11.15 Coffee/tea

11.15-12.00 Daniel Groves Recognizing 3-manifold groups using the word problem Most decision problems for groups are unsolvable in full generality. In order to probe further, we are interested in a `local-to-global' question: Suppose that one can solve the word problem. What properties can then be algorithmically recognized? I will formulate the question precisely (this is somewhat subtle and different interpretations of the question have different answers) and discuss various properties which can (and can't) be recognized modulo the word problem.

The main result is that whether or not a group is the fundamental group of a closed 3-manifold is recognizable modulo the word problem. This is joint work with Jason Manning and Henry Wilton.

12.15-13.00 Jérôme Los Volume entropy for surface groups via dynamics In this talk I will describe a construction based on an idea due to Bowen and Series back in 1979... The construction is new and it enables to obtain a very specific dynamical system on the boundary of surface groups for a large class of presentations. These particular dynamical systems are very special and reflect some properties of the group. These groups are very well known but seen that way gives new perspectives.

13.0-15.00 Lunch

15.00-15.45 Juan Gonzales-Meneses Thurston meets Garside There are two apparently unrelated ways to study braid groups: Algebraically, using Garside normal forms obtained by endowing its elements with a lattice structure, and geometrically, regarding braids as mapping classes and applying Nielsen-Thurston theory. We will present some results, joint with Volker Gebhardt and Bert Wiest, showing some relations between these two approaches: we will see how conjugations which simplify braids algebraically, also simlpify them geometrically, in the case of periodic and reducible braids. We will also present some work in progress with Marta Aguilera, aiming to show that the same holds for pseudo-Anosov braids.

16.00-16.45 Martyn Quick Generators and relations for Thompson's group V Thompson's group V is a famous example of an infinite finitely presented simple group that arises most naturally as particular transformations of the Cantor set. I will describe this group, review some well-known sets of generators and relations for it, and present some new presentations that illustrate how V can be viewed quite naturally as closely linked to the symmetric groups. The latter is joint work with Collin Bleak.

17.0-17.45 Jean-Baptiste Gramain Murnaghan-Nakayama Rules and Perfect Isometries Perfect isometries are the shadow, at the level of characters, of stronger equivalences between blocks of finite groups (such as derived equivalences). In particular, one can give a weaker version of Broué's Conjecture in terms of perfect isometries. M. Enguehard proved in 1988 that any two p-blocks of symmetric groups, which have the same p-weight, are perfectly isometric. The main tool in his proof is given by the Murnaghan-Nakayama Rule, which provides a recursive way of computing character values for the symmetric groups. In this talk, I will present generalisations of this result, as well as applications of them, to groups that are not quite symmetric groups, but do have some analogues of the Murnaghan-Nakayama Rule. This is the case, for example, of the Schur extensions of the symmetric and alternating groups, and of certain wreath products. This is joint work with Olivier Brunat (Paris 7).

Saturday 11 May

10.00-10.45 Pascal Weil On random subgroups of free groups I will survey several notions of randomness for finitely generated subgroups of free groups and finite group presentations, and the asymptotic properties that arise under these notions. Classical results in this field include Gromov-Ol'shanskii-Champetier's result that a random finitely presented group is hyperbolic. The literature has often focused on the "few-generator" model (where a fixed number of generators for subgroups, a fixed number of relators for presentation is considered), or on the density model (with an exponential number of generators/relators). Recent results, obtained with some or all of Bassino, Martino, Nicaud and Ventura, consider intermediate situations, with a polynomial number of generators; or a completely different distribution for subgroups, based on the number of vertices in their Stallings graph.

10.45-11.15 Coffee/tea

11.15-12.00 Sean Cleary Some metric properties of Houghton's groups Houghton's groups are a family of subgroups of permutation groups known for their cohomological properties. Here, I describe some aspects of their geometry and metric properties including families of self-quasi-isomtries. This is joint work with Jose Burillo, Armando Martino and Claas Roever.

12.15-13.00 Emil Sköldberg Multiplicative structures in (co)homology I will begin by giving an introduction to the basics of multiplicative structures in cohomology, in particular in group theory and commutative algebra. Also, I will talk about products in homology, and on resolutions, with mentions on classical results on their existence or non-existence. Finally, I will mention my own recent work on multiplicative structures of minimal free resolutions of edge ideals in a polynomial algebra.

Travel

There are regular rail connections from Dublin to Galway, and bus connections from all Irish cities and towns.
From Dublin airport there are also direct busses to Galway operated by Citylink and GoBus.
Galway Airport seems out of operation, but please check again. There are flights to Shannon from Birmingham, Edinburgh, Heathrow, London City and Manchester by Aer Lingus.

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.

Accommodation

The following hotels and guest houses are convenient for the NUI Galway campus:

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 the organisers Javier Aramayona and Claas Röver.

Groups in Galway 2013 is generously supported by