###### Thursday, September 28, 2017 at 3pm in University Hall (UH) 28

### Mike Davis, Ohio State University

#### Action dimensions of simple complexes of groups

##### Abstract

The geometric dimension of a torsion-free group G is the minimum dimension of a model for BG by a CW complex. Its action dimension is the minimum dimension of a model for BG by a manifold. I will discuss recent work with Kevin Schreve and Giang Le in which we compute the action dimension of Artin groups, graph products and other examples of groups which are given as simple complexes of groups.

###### Tuesday, October 3, 2017 at 3pm in Cockins Hall (CH) 240 **(special day and location)**

### Thomas Koberda, University of Virginia

#### Free products and diffeomorphisms of compact manifolds

##### Abstract

It is a well-known fact that if `G` and `H` are groups of
homeomorphisms of the interval or of the circle, then the free product `G*H`
is also a group of homeomorphisms of the interval or of the circle, respectively. I
will discuss higher regularity of group actions, showing that if `G` and
`H` are groups of `C ^{∞}` diffeomorphisms of the
interval or of the circle, then

`G*H`may fail to act by even

`C`diffeomorphisms on any compact one-manifold. As a corollary, we can classify the right-angled Artin groups which admit faithful

^{2}`C`actions on the circle, and recover a joint result with H. Baik and S. Kim. This is joint work with S. Kim.

^{2}###### Thursday, October 19, 2017 at 3pm in University Hall (UH) 28

### Mark Pengitore, Purdue University

#### Translation-like actions of nilpotent groups

##### Abstract

Whyte introduced translation-like actions of groups which serve as a geometric generalization of subgroup containment. He then proved a geometric reformulation of the von Neumann conjecture by demonstrating a finitely generated group is nonamenable if and only if it admits a translation-like action by a non-abelian free group. This provides motivation for the study of what groups can act translation-like on other groups. As a consequence of Gromov's polynomial growth theorem, only nilpotent groups can act translation-like on other nilpotent groups. In joint work with David Cohen, we demonstrate that if two nilpotent groups have the same growth, but non-isomorphic Carnot completions, then they can't act translation-like on each other.

###### Thursday, November 2, 2017 at 3pm in University Hall (UH) 28

### Sahana Balasubramanya, Vanderbilt University

#### Acylindrical group actions on quasi-trees

##### Abstract

A group `G` is acylindrically hyperbolic if it admits a non-elementary
acylindrical action on a hyperbolic space. We prove that every acylindrically
hyperbolic group `G` has a generating set `X` such that the
corresponding Cayley graph is a (non-elementary) quasi-tree and the action of
`G` on the Cayley graph is acylindrical. Our proof utilizes the notions of
hyperbolically embedded subgroups and projection complexes. As a by-product, we
obtain some new results about hyperbolically embedded subgroups and quasi-convex
subgroups of acylindrically hyperbolic groups.

###### Thursday, November 16, 2017 at 3pm in University Hall (UH) 28

### Kevin Schreve, University of Michigan

#### Action dimension and `L`^{2}-cohomology

^{2}

##### Abstract

The action dimension of a group `G` is the minimal dimension of
contractible manifold that `G` acts on properly discontinuously.
Conjecturally, if a group has nontrivial `L ^{2}` cohomology in
dimension

`n`, the action dimension of

`G`is bounded below by

`2n`. I will discuss this conjecture for graph products of fundamental groups of aspherical manifolds and fundamental groups of complex hyperplane complements. This is joint work with Mike Davis and Giang Le.

###### Thursday, November 23, 2017

### Thanksgiving Break

###### Thursday, November 30, 2017 at 3pm

### Matthew Durham, Yale University

###### Thursday, December 7, 2017 at 3pm

### Priyam Patel, UC Santa Barbara

###### Thursday, December 14, 2017 at 3pm

#### Open (finals week)

###### Thursday, April 5, 2018

### Rita Gitik, University of Michigan

#### A new algorithm in group theory

##### Abstract

We describe a new algorithm which determines if the intersection of a quasiconvex subgroup of a negatively curved group with any of its conjugates is infinite. The algorithm is based on the concepts of a coset graph and a weakly Nielsen generating set of a subgroup. We also give a new proof of decidability of a membership problem for quasiconvex subgroups of negatively curved groups.