The GT seminar meets on Fridays
in Math. 520,
at 1:15PM.

Organizer:
Walter Neumann.

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

## Spring 2014

## Fall 2014

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

TBA | Jane Gilman | TBA |

TBA | David Shea Vela-Vick | TBA |

## Abstracts.

**January 31**:
Jason Behrstock:
“Higher dimensional filling and divergence for mapping class
groups.”
**Abstract**:
We will discuss filling and divergence functions. We will
describe their behaviors for mapping class groups of surfaces and
show that these functions exhibit phase transitions at the rank, in
analogy to the corresponding result for symmetric spaces. This work
is joint with Cornelia Drutu.

**February 7**:
BoGwang Jeon:
“Hyperbolic three maniflds of bounded volume and trace field degree II”
**Abstract**:A year ago, in the same seminar
(http://math.columbia.edu/~gtseminar/S2013.html#BJ), I proposed a way to
attack the conjecture that there are only finitely many hyperbolic three
manifolds of bounded volume and trace field degree. In this talk, I will go
over the previous talk and present further results and related questions. No
further background will be necessary but it will be good to know about
Thurston's Dehn filling theorem.

**February 14**:
Mina Teicher
“Line Arrangements -Topology, Combinatorics and application to Algebraic
Surfaces”
**Abstract**:
In this talk Topology means Fundamental Group of the complement of
the line arrangement, and Combinatorics means the Lattice of the
arrangement or its Graph.
I will review the history of the problem of Topology vs. Combinatorics of
line arrangements, give the state of the art as well as reporting on work
in Progress. I'll conclude with applications to Topology of Algebraic
Surfaces.

**February 21**:
Bill Menasco
“Short distances in the curve complex”
**Abstract**:
We will give a preliminary report on recent joint work with Dan Margalit and Joan Birman. The focus is an algorithm for determining
whether a filling pair of curves in an orientable closed surface of genus greater than 1 has distance 3, 4, 5 or bigger. The algorithm is a natural
generalization of John Hempel's distance 3 algorithm (unpublished) and a significant improvement of the previously know algorithms of Leasure and Shackleton for determining the distance between two curves in the curve complex. As an application of the algorithm we will give newly discovered distance 4 pairs of curves in genus 2 and 3 surfaces.

**February 28**:
Adam Levine:
“Non-orientable surfaces in homology cobordisms”
**Abstract**:We study the minimal genus problem for embeddings of closed, non-orientable
surfaces in a homology cobordism between rational homology spheres, using obstructions
derived from Heegaard Floer homology and from the Atiyah-Singer index theorem. For
instance, we show that if a non-orientable surface embeds essentially in the product of a
lens space with an interval, its genus and normal Euler number are the same as those of a
stabilization of a non-orientable surface embedded in the lens space itself. This is
joint work with Danny Ruberman and Saso Strle.

**March 14**:
Jingyin Huang
“Quasi-isometry classification of right-angled Artin group with
finite outer automorphism group”
**Abstract**:
Let G and G' be two right-angled Artin groups with finite outer
automorphism group, we show they are isomorphic iff they are
quasi-isometric. If we only assume Out(G) is finite, then G' can be
realized as a subgroup of finite index in G, and there is a correspondence
between such G' and compact convex subcomplexes in the Salvetti complex of
G, which can be thought as a nice fundamental domain for G'.

**March 28**:
Marc Culler
“Character varieties of knot complements
**Abstract**:
I will survey some known connections between knot invariants and
character varieties, framed in terms of a computable object called
the PE character variety, which includes the SU(2) character variety
but is defined in terms of the SL(2,C) character variety.

**April 4**:
Tarik Aougab:
“Minimally intersecting filling pairs on surfaces”
**Abstract**:
Let S_{g} denote the closed orientable surface of genus g. We show
the existence of exponentially many mapping class group orbits of
pairs of simple closed curves on S_{g} which fill the surface, and
intersect minimally amongst all filling pairs. We will demonstrate
the main idea of the construction, and discuss applications of
minimally intersecting filling pairs to understanding how the coarse
geometry of the curve complex explicitly depends on the topology of
the underlying surface.

**April 11**:
Tom Church:
“A survey of representation stability”
**Abstract**:
I will give a gentle survey of the theory of representation stability, viewed through the lens of its applications. These applications include: homological stability for configuration spaces of manifolds; understanding the stable (and unstable) homology of arithmetic lattices; Hecke eigenclasses in stable mod-p cohomology; uniform generators for congruence subgroups and "congruence" subgroups; and distributional stability for random squarefree polynomials over finite fields.

**April 25**:
Matthew Day:
“An infinite presentation for the Torelli subgroup IA_n of the
automorphism group of a free group”
**Abstract**:
I will describe joint work with Andy Putman, in progress, in which we
verify the group presentation described in the title. �This infinite
presentation is a "finite L-presentation", meaning that it has
finitely many generators, finitely many basic relations, and a
sufficient set of relations is given by the orbit of the basic
relations under the action of a finitely generated monoid. �The proof
involves the action of Aut(F_n) on a curve complex analog, and also
uses the theory of group extensions. �As corollaries, we obtain
several results about the second homology H_2(IA_n).

**May 2**:
David Fisher:
“Quasi-isometric embeddings: rigidity and examples”
**Abstract**:
We study quasi-isometric embeddings of higher rank
symmetric spaces into one another. This generalizes both
Mostow-Margulis rigidity and the rigidity of self-quasi-isometries of
these spaces (Kleiner-Leeb, Eskin-Farb). I will present some rigidity
results (which were to be expected) as well as some surprising
examples. I will end the talk with several open problems. This is
joint work with Kevin Whyte.

**May 9**:
Adam Giambrone:
“Semi-Adequate Link Diagrams and Hyperbolic Volume Estimates”
**Abstract**:
In this talk we will explore some ways to bound the volume of the complement of certain hyperbolic, semi-adequate links. First, we find volume bounds that can be expressed in terms of two diagrammatic quantities: the twist number and the number of certain alternating tangles in a semi-adequate link diagram. Second, we express these volume bounds in terms of a single coefficient of the colored Jones polynomial of the link. Consequently, we are able to provide a number of families of links that satisfy a Coarse Volume Conjecture. The two main families of links that we will consider are closures of braids and plat closures of braids.

# Other relevant information.

## Previous semesters:

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.

## Our e-mail list.

Announcements for this seminar, as well as for related seminars and events, are sent to the GT seminar mailing list. You can subscribe directly or by contacting Walter Neumann.