12:30-13:45 lunch in The Court Inn. This is located on Court Lane (see the map ).
I will discuss a conjecture that states that except in dimension n=3, the complete hyperbolic n-manifold of the smallest volume is noncompact. This is a joint work with Misha Belolipetsky.
We investigate the quasi-isometry classification of certain one-ended word-hyperbolic Coxeter groups. Our main result uses Bowditch's JSJ decomposition of one-ended hyperbolic groups to give a complete classification of an infinite family. From this and a theorem of Crisp and Paoluzzi, it follows that for these groups, quasi-isometry is stronger than commensurability. This is joint work with Pallavi Dani.
The notion of an acylindrically hyperbolic group was recently introduced by Denis Osin, who proved that this class of groups coincides with some other classes previously studied by Bestvina-Fujiwara,
Hamenstadt and Dahmani-Guirardel-Osin. The primary goal was to generalize the class of (relatively) hyperbolic groups in the sense of Gromov, extending the 'negatively curved' techniques to cover many groups that could not be handled by such methods previously. For instance, by the work of Dahmani, Guirardel and Osin, Aut(F_n) is acylindrically hyperbolic if n>1, where F_n is the free group of rank n. The same holds for all but finitely many mapping class groups of compact surfaces.
During the talk I will define acylindrically hyperbolic groups, listing some of their basic properties. Then I will discuss criteria which, given a group G acting on a simplicial tree, imply that G is acylindrically hyperbolic. I will also mention some applications of this criterion to 1-relator groups, graph products and fundamental groups of 3-manifolds. The talk will be based on a joint work with Denis Osin.
Room CM107 is on the ground floor, to the felt from tyhe main entrance.
There will be an early dinner in Durham. Please e-mail Anna Felikson if you want to attend.