Titles and abstracts​

 

Friday, May 17th (room 103)

• 15:00 - 15:50 Dario Ascari (University of the Basque Country)

The Dehn function of subdirect products of free groups

 

Subgroups of direct products of free groups can be very wild in general; however, they become much more controlled once they are required to satisfy some finiteness condition.

 

We investigate the Dehn function of such groups, which represents the complexity of solving the word problem. We show that, for subgroups of type F_{n-1} in a product of n factors, there is a uniform polynomial bound of N^9 on all the Dehn functions. We also show an example of a subgroup whose Dehn function is exactly N^4; the computation is based on an invariant built using braid groups.

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• 16:00 - 16:50 Dominik Francoeur (Newcastle University)

Intersection-saturated groups and groups with micro-supported actions

 

A group is said to possess the Howson property if the intersection of any two finitely generated subgroups is again finitely generated. When a group fails to have the Howson property, one can try to characterise how far it is from having it. Such considerations give rise to the notion of intersection-saturated groups, introduced recently by Delgado, Roy and Ventura.

 

In this talk, we'll see a new construction for intersection-saturated groups based on so-called micro-supported actions, that allows one in particular to produce finitely presented amenable examples.

 

• 17:00 - 17:50 Marco Linton (University of Oxford)

The relation gap and relation lifting problems for groups with cyclic relation modules

 

If F is a free group and F/N is a presentation of the group G, there is a natural way to turn the abelianisation of N into a left ZG-module, known as the relation module of the presentation. A presentation F/N is said to have relation gap if its relation module has strictly fewer ZG-module generators than N has normal generators.

 

Infinite relation gaps were found by Bestvina--Brady, but the existence of finite relation gaps remains an open problem, closely related with questions on the homotopy types of 2-complexes such as Wall's D(2) problem. I will first motivate the problem and survey what is known and what is not known. Then I will present a solution to the relation gap and relation lifting problems for certain groups with cyclic relation module.

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Saturday, May 18th (room 103)

• 11:00 - 11:50 Armando Martino (University of Southampton)

TBA

 

TBA.

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• 12:00 - 12:50 Yuri Santos (University of Lincoln)

TBA

 

TBA.

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