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 |
---|---|---|

Friday Sept 9 | Organizational meeting | 2pm Room 520 |

September 16 | Hung C Tran (UGA) | Geometric embedding properties of Bestvina-Brady subgroups |

September 22 Thursday 2:40pm | BoGwang Jeon | The Unlikely Intersection Theory and the Cosmetic Surgery Conjecture |

September 30 | No GT seminar | |

October 7 | Henry Segerman, Oklahoma State | Connectivity of triangulations without degree one edges under 2-3 and 3-2 moves |

October 14 | Mehdi Yazdi (Princeton) | On Thurston's Euler class one conjecture |

October 21 | David Hume, MSRI and Oxford | The wide world of relative hyperbolicity |

October 28 | Linus Kramer, Universitaet Muenster | Automatic continuity of abstract homomorphisms between topological groups |

November 4 | No GT Seminar | Symplectic Seminar |

November 11 | Tim Susse, U Nebraska | Geometry of the word problem in 3-manifold groups |

November 17 Thursday 2:40pm | Brendan Owens, Glasgow University | Searching for slice alternating knots |

November 18 | Daniel Groves, UIC | Hyperbolic groups acting improperly |

November 25 | No Seminar | Happy Thanksgiving |

December 1 Thursday 2:40pm | Cornelia Drutu, Oxford University | Strong versions of Kazhdan's Property (T) and random groups |

December 2 | David Futer, Temple U | Abundant quasifuchsian surfaces in cusped hyperbolic 3-manifolds |

December 8 Thursday 2:40pm | Corey Bregman, Rice | Kaehler Groups and Surface Bundles over Tori |

December 9 | Hongbin Sun, UCB | NonLERFness of arithmetic hyperbolic manifold groups |

December 15 Thursday 2:40pm | Nick Salter, Chicago | On the monodromy group of the family of smooth plane curves |

## Abstracts

**Hung C Tran**, UGA

September 16

**Title**: Geometric embedding properties of Bestvina-Brady subgroups

We compute the subgroup distortion of Bestvina-Brady subgroups. We use
the result of this computation to show that for each integer $n\geq
3$, there is a free subgroup of rank $n$ of some right-angled Artin
group whose inclusion is not a quasi-isometric embedding. This
corollary answers the question of Carr about the minimum rank $n$ such
that some right-angled Artin group has a free subgroup of rank $n$
whose inclusion is not a quasi-isometric embedding. It is
also well-known that a right-angled Artin group $A_\Gamma$ is the
fundamental group of a graph manifold whenever the defining graph
$\Gamma$ is a tree. We show that the Bestvina-Brady subgroup
$H_\Gamma$ in this case is a horizontal surface subgroup.

**BoGwang Jeon**, Columbia

THURSDAY September 22, 2:40pm

**Title**: The Unlikely Intersection Theory and the Cosmetic Surgery Conjecture

The main result of this talk is the following theorem:
Let M be a 1-cusped hyperbolic 3-manifold whose cusp shape is not quadratic, and M(p/q) be its p/q-Dehn filled
manifold. If p/q is not equal to p'/q' for sufficiently large |p|+|q| and |p'|+|q'|, there is no orientation
preserving isometry between M(p/q) and M(p'/q').
This resolves the conjecture of C. Gordon, which is so called the Cosmetic Surgery Conjecture, for hyperbolic
3-manifolds belonging to the aforementioned class except for possibly finitely many exceptions for each manifold. We
also consider its generalization to more cusped manifolds. The key ingredient of the proof is the unlikely
intersection theory developed by E. Bombieri, D. Masser, and U. Zannier.

**Henry Segerman**, Oklahoma State U

October 7

**Title**: Connectivity of triangulations without degree one edges under 2-3 and 3-2
moves.

Matveev and Piergallini independently showed that, with a small number of known
exceptions, any triangulation of a three-manifold can be transformed into any
other triangulation of the same three-manifold with the same number of vertices,
via a sequence of 2-3 and 3-2 moves. We can interpret this as showing that the
"2-3 Pachner graph" of such triangulations is connected. This is useful for
defining invariants of a three-manifold based on the triangulation. However, there
are "would-be" invariants that can only be defined on triangulations with certain
properties, for example 1-efficiency or having only essential edges.
Unfortunately, there are no similar connectivity results for the subgraphs of the
Pachner graph with such properties. In this talk, I will describe a new
connectivity result for a weaker property than either 1-efficiency or essential
edges: that of a triangulation having no degree one edges.

**Mehdi Yazdi**, Princeton

October 14

**Title**: On Thurston's Euler class one conjecture

In 1976, Thurston proved that taut foliations on closed hyperbolic 3–manifolds have Euler class of norm at most one, and conjectured that, conversely, any
Euler class with norm equal to one is Euler class of a taut foliation. I construct counterexamples to this conjecture and suggest an alternative conjecture.

**David Hume**, MSRI and Oxford

October 21

**Title**: The wide world of relative hyperbolicity

I will describe part of a joint project with Matthew Cordes in
which, for a given finitely generated group $H$ satisfying some very mild
assumptions, we build infinitely many quasi-isometry types of 1-ended groups
$G_i$ which are hyperbolic relative to $H$. With care, one can even ensure
that all the $G_i$ satisfy Kazhdan's property T. The invariant we use is a
refinement of the stable dimension which we introduced in a previous paper.

**Linus Kramer**, Univ Muenster

October 28

**Title**: Automatic continuity of abstract homomorphisms between topological groups

It is a classical result that an ’abstract’ group isomorphism between
real semisimple Lie groups is automatically continuous. In this talk
we consider more generally abstract homomorphisms of certain
topological groups onto certain types of Lie groups and compact
groups. The approach is axiomatic and yields new continuity results
both for Polish and for locally compact groups.

**Tim Susse**, University of Nebraska

November 11

**Title**: Geometry of the word problem in 3-manifold groups

Since the introduction of automatic groups, there have been
attempts by many mathematicians to find a common solution to the word
problem in any 3-manifold groups that uses only a finite state automaton.
However, not all 3-manifold groups are automatic. Several generalizations of
automaticity have been introduced, including the notion of an autostackable
group by Brittenham, Hermiller and Holt. We will define autostackability, as
well as autostackability respecting a subgroup and prove that the
fundamental group of any closed 3-manifold is autostackable.

**Brendan Owens**, Glasgow University

November 17

**Title**: Searching for slice alternating knots

Many geometric properties of alternating knots have been shown to be computable or discernible from their alternating diagrams. This talk is based on the possibility
that sliceness of an alternating knot may be algorithmically detectable from an alternating diagram. I will describe a computer search which has found approximately 29,000 new
slice alternating knots, and discuss its limitations and some related questions. This is joint work with Frank Swenton.

**Daniel Groves**, University of Illinois at Chicago

November 18

**Title**: Hyperbolic groups acting improperly

Suppose that a hyperbolic group G acts cocompactly on a CAT(0)
cube complex,
and that vertex stabilizers are quasiconvex and virtually special. Then G
is virtually special.
In case vertex stabilizers are finite, this is a result of Agol (which
implies the Virtual
Haken Conjecture and the Virtual Fibering Conjecture), and in case the cube
complex is
a tree it is a result of Wise (a key ingredient in Agol's proof and result
with significant
consequences in its own right). I will discuss the background and
ingredients of the proof of this result
and also some possible applications. This is joint work with Jason Manning
(Cornell).

**Cornelia Drutu**, Oxford University

December 1, 2:40pm

**Title**: Strong versions of Kazhdan's Property (T) and random groups

Various strengthened versions of property (T) have been
formulated in recent years. Among them, those involving actions on Lp
spaces are particularly interesting, because they manage to achieve
a separation between rank one and higher rank lattices, because of their
presumed connection to the conformal dimension of the boundary of hyperbolic
groups,
and because of the increasing role that they play in operator algebras.
In this talk I shall explain how random groups have all the strengthened Lp
-versions of property (T), and how these connect to the conformal dimension
of their boundary. This is joint work with J. Mackay.

**David Futer**, Temple University

December 2

**Title**: Abundant quasifuchsian surfaces in cusped hyperbolic 3-manifolds

I will discuss a proof that every finite volume hyperbolic 3-manifold M contains an abundant collection of
immersed, $\pi_1$-injective surfaces. These surfaces are abundant in the sense that their lifts to the universal
cover separate any pair of disjoint geodesic planes. The proof relies in a major way on the corresponding theorem of
Kahn and Markovic for closed 3-manifolds. As a corollary, we recover Wise's theorem that the fundamental group of M
is acts properly and cocompactly on a cube complex. This is joint work with Daryl Cooper.

**Corey Bregman**, Rice

December 8

**Title**: Kaehler Groups and Surface Bundles over Tori

Abstract: A question going back to Serre asks which finitely presented
groups arise as the fundamental groups of compact Kaehler manifolds. In
this talk we study extensions of abelian groups by hyperbolic surface
groups. Topologically, these groups are realized as fundamental groups of
surface bundles over tori. We show that if any such an extension is
Kaehler, then it is virtually a product. This is joint work with Letao
Zhang.

**Hongbin Sun**, UCB

December 9

**Title**: NonLERFness of arithmetic hyperbolic manifold groups

Abstract: We will show that, for "almost" all arithmetic hyperbolic
manifolds with dimension >3, their fundamental groups are not LERF. The
main ingredient in the proof is a study of certain graph of groups with
hyperbolic 3-manifold groups being the vertex groups. We will also show
that a compact irreducible 3-manifold with empty or tori boundary does not
support a geometric structure if and only if its fundamental group is not
LERF.

**Nick Salter**, Chicago

December 15

**Title**: On the monodromy group of the family of smooth plane curves

Abstract: Let P denote the space of smooth projective curves in the
complex projective plane of degree d. Over P, there is the tautological
family of smooth plane curves, and hence a monodromy representation, i.e.
a subgroup of the mapping class group. In the 1980?s, algebraic geometers
computed an ?approximation? to this monodromy group, namely the action on
the homology of the fiber. I will discuss some recent work of mine
concerning a characterization of the image of the full monodromy
representation, including a complete description of the image for degree
d=5, as well as a conjectural picture of the image for all degrees. This
will involve a blend of ideas from algebraic geometry and the theory of
the mapping class group, particularly the Torelli group.

# Other relevant information.

## Previous semesters:

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.