###### 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 `L`^{2} cohomologies

^{2}

##### 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
`L ^{2}` 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 `L ^{2}` 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 `RP`^{3}-structures on `3`-orbifolds

^{3}

##### 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.