Cohomological methods in geometric group theory (12w5080)
Benson Farb (University of Chicago)
Dave Morris (University of Lethbridge)
Graham Niblo (University of Southampton)
Karen Vogtmann (Cornell University)
This workshop will bring together experts from three areas of mathematics in which cohomological methods have recently played a fundamental role: geometric group theory, non-commutative geometry and coarse geometry. Principle topics will include:
i) Representation stability, as introduced by Church and Farb in order to expand the important and well-studied concept of homological stability to a far broader context.
ii) The proof of the Borel, and Farrell-Jones conjectures by Lueck and Bartels for hyperbolic groups and CAT(0) groups.
iii) Bounded cohomology, amenability and generalisations, motivated by the recent work of Burger-Iozzi-Wienhard, Monod, Calegari and others illustrating its power to solve problems in diverse areas, including rigidity, orbit equivalence and amenability.
This workshop will take place more than 5 years after the last conference on homological methods in group theory (Oberwolfach, April 2006). That conference preceded much of the development (i)-(iii), so another meeting is well due. Further evidence of the need for such a meeting was provided at the more recent Oberwolfach meeting (Non-positive Curvature and Geometric Structures in Group Theory, April 2010) at which Bartels' talks attracted considerable attention from geometric group theorists keen to engage with problems in high dimensional topology.
We will plan the schedule to allow extensive time for informal interactions, during which workers in different areas can share ideas and methods. There will be a limited number of main talks in which leading experts in each of the areas will outline recent progress, with specific attention paid to open questions, the new tools recently developed and future directions. These talks are intended to foster further interaction. Bearing in mind the value of graduate student and postdoctoral training, there will be a few optional sessions at which the more basic ideas underpinning recent progress will be outlined. Such sessions have been profitably introduced at other recent meetings including the Banach Centre meetings on geometric group theory at Bedlewo and the Bristol-Oxford-Southampton seminar in geometric group theory. They have been highly valued by the participants.
In selecting the final participant list particular attention will be paid to members from under-represented groups. In addition to the several female and African American participants who are already slated to speak, many young people working in the area are female and we will actively seek to involve them in the workshop.