The GT seminar meets on Fridays
in Math
520, at 2 PM (overflow seminars Thursday 2:40pm Room 507).

Organizer:
Walter Neumann.

Other
area seminars. Our e-mail
list. Archive of previous semesters

Date | Speaker | Title |
---|---|---|

January 20 | Organizational Meeting | Room 520, 2pm |

February 3 | Victoria Akin, Chicago | Point-pushing in the mapping class group |

February 9, 2:40pm Room 507 |
Dani Wise | A graph coloring problem and its algebraic and topological consequences |

February 10 POSTPONED, SNOW | Jonah Gaster, Boston College | Combinatorial properties of curve graphs |

February 17 | Sarah Mousley, U. Illinois | Boundary maps for some hierarchically hyperbolic spaces |

February 24 | Carolyn Abbott, CUNY and Wisconsin | Universal acylindrical actions |

March 3 | Feng Luo, Rutgers | TBA |

March 10 | Anh Tran, UT Dallas | The topology of the Jones polynomial |

March 17 | No seminar | Spring break |

March 24 | Xinghua Gao, Illinois | TBA |

March 31 | Ilya Kofman, CUNY | TBA |

April 7 | Matthew Stover | TBA |

April 14 | TBA | TBA |

April 21 | TBA | TBA |

April 28 | Kevin Kordek, TAMU | TBA |

## Abstracts

**Victoria Akin**, Chicago

February 3

**Title**: Point-pushing in the mapping class group

The point-pushing subgroup of the mapping class group of a surface
with a marked point can be considered topologically as the subgroup
that pushes the marked point about loops in the surface. Birman, who
discovered the point-pushing map, showed that this subgroup is
abstractly isomorphic to the fundamental group of the surface,
\pi_1(S). We can characterize this point-pushing subgroup
algebraically as the only normal subgroup inside of the mapping class
group isomorphic to \pi_1(S). This uniqueness allows us to recover a
description of the outer automorphism group of the mapping class
group.

**Dani Wise, Room 507**

February 9, 2:40pm

**Title**: A graph coloring problem and its algebraic and
topological consequences.

I will first describe a simple graph coloring problem and survey
some examples of graphs for which the coloring problem has or has no
solution. I will then give a quick introduction to Bestvina-Brady Morse
theory. Finally, I will describe the relationship between the coloring
problem and some amusing virtual algebraic fibering consequences for
geometric group theory and hyperbolic 4-manifolds. This is joint work with
Kasia Jankiewicz and Sergey Norin.

**Jonah Gaster**, Boston College

February 10

**Title**: Combinatorial properties of curve graphs

The curve graph of a closed oriented surface of genus $g$ has
vertices given by simple closedÂ curves, and edges that correspond
to curves that can be realized disjointly. Inquiry into the large scale
geometry of these graphs has borne considerable fruit, and lead to the
resolution of some of Thurston's conjectures. We will take a more naive
perspective and explore instead combinatorial properties of this graph. For
instance, what is its chromatic number (finite due to work of
Bestvina-Bromberg-Fujiwara)? What are its induced subgraphs? Though precise
answers to these questions are currently beyond reach, we will present
progress that informs them. In particular, in joint work with Josh Greene
and Nick Vlamis we show that the
separating curve graph has chromatic number coarsely equal to $g \log(g)$,
and the subgraph spanned by vertices in a fixed non-zero homology class is
uniquely $g-1$-colorable.

**Sarah Mousley**, U. Illinois

February 17

**Title**: Boundary maps for some hierarchically hyperbolic spaces

There are natural embeddings of right-angled Artin groups $G$
into the mapping class group $Mod(S)$ of a surface $S$. The groups $G$ and
$Mod(S)$ can each be equipped with a geometric structure called a
hierarchically hyperbolic space (HHS) structure, and there is a notion of a
boundary for such spaces. In this talk, we will answer the following
question: does every embedding $\phi: G \rightarrow Mod(S)$ extend
continuously to a boundary map $\partial G \rightarrow \partial Mod(S)$?
That is, given two sequences $(g_n)$ and $(h_n)$ in $G$ that limit to the
same point in $\partial G$, do $(\phi(g_n))$ and $(\phi(h_n))$ limit to the
same point in $\partial Mod(S)$? No background in HHS structures is needed.

**Carolyn Abbott**, CUNY and Wisconsin

February 24

**Title**:Universal acylindrical actions

The class of acylindrically hyperbolic groups, which are groups
that admit a certain type of non-elementary action on a hyperbolic
space, contains many interesting groups such as non-exceptional
mapping class groups and Out(F_n) for n>1. In such a group, a
generalized loxodromic element is one that is loxodromic for some
acylindrical action of the group on a hyperbolic space. Given a
finitely generated group, one can look for an acylindrical action on a
hyperbolic space in which all generalized loxodromic elements act
loxodromically; such an action is called a universal acylindrical
action. I will discuss recent results in the search for universal
acylindrical actions, describing a class of groups for which it is
always possible to construct such an action as well as an example of a
group for which no such action exists.

**Feng Luo**, Rutgers

March 3

**Title**:

**Anh Tran**, UT Dallas

March 10

**Title**: The topology of the Jones polynomial

We will discuss old and new conjectures about the topology of the Jones polynomial.

These include the AJ conjecture, slope conjecture, and strong slope conjecture.

The AJ conjecture of Garoufalidis relates the A-polynomial and the colored Jones polynomial of a knot. The
A-polynomial was introduced by Cooper et al. in 1994 and has been fundamental in geometric topology. A similar
conjecture to the AJ conjecture was also proposed by Gukov from the viewpoint of the Chern-Simons theory. The slope
conjecture of Garoufalidis and a new conjecture of Kalfagianni and the speaker are about the relationship between
the degree of the colored Jones polynomial of a knot and the topology of the knot.

These conjectures assert that certain boundary slopes and Euler characteristics of essential surfaces in a knot
complement can be read off from the degree of the colored Jones polynomial.

**Xinghua Gao**, Illinois

March 24

**Title**:

**Ilya Kofman**, CUNY

March 31

**Title**:

**Matthew Stover**, Temple

April 7

**Title**:

**Kevin Kordek**, TAMU

April 28

**Title**:

# Other relevant information.

## Previous semesters:

Fall 2016, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, 2010/11, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006.## Other area seminars.

- Columbia Symplectic Geometry/Gauge Theory Seminar
- All Columbia Math Dept Seminars
- CUNY Geometry and Topology Seminar
- CUNY Complex Analysis & Dynamics Seminar
- CUNY Magnus Seminar
- Princeton Topology Seminar.