Thursday, September 6, 2012 at 3pm in CH (Cockins Hall) 240
Raeyong Kim, Ohio State University
Algebraic Rank of Right-Angled Coxeter Groups
Abstract
Following Prasad and Raghunathan, the notion of the algebraic rank of a group will be introduced. I will show that any infinite irreducible non-affine right-angled Coxeter group W has an algebraic rank of 1. As a corollary, we provide a partial answer to the question about the commensurability of Coxeter groups. Namely, W is not commensurable to any uniform lattice in a higher rank non-compact connected semi-simple Lie group.
Thursday, September 13, 2012 at 3pm in CH (Cockins Hall) 240
Izhar Oppenheim, Ohio State University
Criteria for Kazhdan property (T) and vanishing of L2 cohomologies
Abstract
This talk will have several aims – the first is to introduce property (T) using several definitions that will be equivalent in our setting (namely unitary representations definition, property (FH) and the vanishing of the first L2 cohomology). The second is to present some geometrical criteria for property (T) in the case of a group acting on 2 dimensional simplicial complex. The third (if time permits), is to discuss criteria for property (T) when the dimension of the simplicial complex is higher than 2.
No prior knowledge on property (T) or L2 cohomologies will be assumed.
Thursday, September 20, 2012 at 3pm in CH (Cockins Hall) 240
Tam Nguyen-Phan, Ohio State University
Finite volume, negatively curved manifolds
Abstract
I will discuss the topology of noncompact, complete, finite volume, negatively curved manifolds. Specifically, how different conditions on the curvature control the topology of these manifolds. There will be a lot of examples.
Thursday, October 18, 2012 at 3pm in CH (Cockins Hall) 240
Yulan Qing, Tufts University
Boundaries of a CAT(0) complex
Abstract
We study the ideal boundary of the universal cover of a torus complex proposed by Croke and Kleiner. We show that a subtle change in the geometric data of the group action yield different homeomorphism types of its boundary. We also show that, the core component of the boundary, i.e. the union of all circles, behaves nicely with respect to certain quasi-isometries. Lastly, we show that if a right-angled Coxeter groups acting geometrically on this complex, then the action of generators are necessarily at right angles.
Thursday, October 25, 2012 at 3pm in CH (Cockins Hall) 240
Suhyoung Choi, KAIST
Deforming convex RP3-structures on 3-orbifolds
Abstract
We consider n-orbifolds modeled on real projective geometry. These include hyperbolic manifolds and orbifolds. There are nontrivial deformations of hyperbolic orbifolds to real projective ones. We will present some Coxeter 3-orbifolds that we can understand the deformations, and we will discuss various results about the open convex real projective 3-orbifolds with radial ends and their deformation spaces. Lastly, we will end with the classification problem of the radial ends of convex real projective n-orbifolds.