Thursday, September 25, 2014 at 3:00pm in Math Tower (MW) 154
Russell Ricks, University of Michigan
Flat strips in rank one CAT(0) spaces
Abstract
Let X be a proper, geodesically complete CAT(0) space under a geometric (that is, properly discontinuous, cocompact, and isometric) group action on X; further assume X admits a rank one axis. Using the Patterson-Sullivan measure on the boundary, we construct a generalized Bowen-Margulis measure on the space of geodesics in X. However, in order to construct this measure, we must prove a couple structural results about the original CAT(0) space X. First, with respect to the Patterson-Sullivan measure, almost every point in the boundary of X is isolated in the Tits metric. Second, under the Bowen-Margulis measure, almost no geodesic bounds a flat strip of any positive width. Then, with the generalized Bowen-Margulis measure, we can characterize when the length spectrum of X is arithmetic (that is, the set of translation lengths is contained in a discrete subgroup of the reals). In this talk, we will discuss the constructions and some of the issues involved.
Tuesday, September 30, 2014 at 1:45pm in Cockins Hall (CH) 240
Nathan Broaddus, Ohio State University
Tuesday, October 7, 2014 at 1:45pm in Cockins Hall (CH) 240
Barry Minemyer, Ohio State University
Tuesday, October 14, 2014 at 1:45pm in Cockins Hall (CH) 240
Izhar Oppenheim, Ohio State University
Tuesday, October 21, 2014 at 1:45pm in Cockins Hall (CH) 240
Mike Davis, Ohio State University
The action dimension of RAAGs
Abstract
This is a report on joint work with Grigori Avramidi, Boris Okun and Kevin Schreve. The "action dimension" of a discrete group G is the smallest dimension of a contractible manifold which admits a proper action of G.
Associated to any flag complex L there is a right-angled Artin group, AL. We compute the action dimension of AL for many L.
Our calculations come close to confirming the conjecture that if the L2-Betti number of AL in degree l is nonzero, then the action dimension of AL is greater than or equal to 2l.