The GT seminar meets on Fridays
in Math 520,
at 2 PM.

Organizer:
Abhijit Champanerkar.

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

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

September 11 | Organizational meeting | 2pm Room 520 |

September 18 | Daryl Cooper (UCSB & IAS) | Deforming Convex Projective Manifolds |

September 25 | Balazs Strenner (IAS) | Algebraic degrees and Galois conjugates of pseudo-Anosov stretch factors |

October 2 | Anastasiia Tsvietkova (UC Davis) | The number of surfaces of fixed genus in an alternating link complement |

October 9 | No Seminar | Workshop on Geometric Structures on 3-Manifolds, IAS Princeton |

October 16 | Joseph Maher (CSI & GC, CUNY) | Random walks on weakly hyperbolic groups |

October 23 | No seminar | |

October 30 | Tye Lidman (UT Austin & IAS) | Quasi-alternating links with small determinant |

November 6 | Joel Hass (UC Davis & IAS) | Invariants of Random Knots |

November 13 | Cameron Gordon (UT Austin) | Taut foliations, left-orderability and cyclic branched coverings |

November 20 | Christian Zickert (Maryland) | Triangulation independent Ptolemy varieties |

November 27 | No Seminar | Thanksgiving |

December 4 | Andrei Vesnin (Chelyabinsk, Russia) | Around right-angled hyperbolic polyhedra |

December 11 | No seminar |

## Abstracts

**Daryl Cooper**, UCSB & IAS

September 18th, 2015

**Title**: Deforming Convex Projective Manifolds

**Abstract**: This talk concerns a properly convex real
projective manifold with (possibly empty) compact, strictly convex
boundary, and which consists of a compact part plus finitely many
generalized cusps. We extend a theorem of Koszul which asserts that
for a compact manifold without boundary the holonomies of properly
convex structures is an open subset of the representation variety.

**Balazs Strenner**, IAS

September 25th, 2015

**Title**: Algebraic degrees and Galois conjugates of pseudo-Anosov
stretch factors

**Abstract**:
Thurston showed that the algebraic degrees of stretch factors of
pseudo-Anosov maps on the orientable surface of genus g are bounded by
6g-6. He claimed that his Dehn twist construction produces examples of
maximal 6g-6 degree stretch factors, but he did not give a proof. I
will discuss a method based on a construction of Penner that produces
maximal degree examples, and also examples of all even degrees less
than 6g-6. I will also mention related work with Hyunshik Shin, where
we study Galois conjugates of stretch factors, and use this to resolve
a conjecture of Penner.

**Anastasiia Tsvietkova**, UC Davis

October 2nd, 2015

**Title**: The number of surfaces of fixed genus in an alternating
link complement

**Abstract**: Let $L$ be a prime alternating link with $n$
crossings. We show that for each fixed $g$, the number of genus $g$
incompressible surfaces in the complement of $L$ is bounded by a
polynomial in $n$. Previous bounds were exponential in $n$. This is
joint work with Joel Hass and Abigail Thompson.

**Joseph Maher**, CSI & GC, CUNY

October 16th, 2015

**Title**: Random walks on weakly hyperbolic groups

**Abstract**: Let G be a group acting by isometries on a Gromov
hyperbolic space, which need not be proper. If G contains two
hyperbolic elements with disjoint fixed points, then we show that a
random walk on G converges to the boundary almost surely. This gives a
unified approach to convergence for the mapping class groups of
surfaces, Out(F_n) and acylindrical groups. This is joint work with
Giulio Tiozzo. We will also discuss some work in progress on
applications to 3-manifolds.

**Tye Lidman**, UT Austin & IAS

October 30th, 2015

**Title**: Quasi-alternating links with small determinant

**Abstract**: Quasi-alternating links are a generalization of alternating links as a natural class of links with simple Floer and Khovanov homologies. Greene classified the quasi-alternating links with determinant at most 3, and Teragaito classified the determinant 5 links. We will extend this classification further and study some Dehn surgery problems along the way. This is joint work with Steven Sivek.

**Joel Hass**, UC Davis & IAS

Nov 6th, 2015

**Title**: Invariants of Random Knots

**Abstract**: I will discuss a model for generating random knots
called the Petaluma model. This model is based on
the petal diagram of a knot, introduced by Adams.
In this model we obtain exact formulas for the distribution of the linking
number of a random 2-component link, as well as for
the moments of the distribution of the Casson invariant and other
finite type invariants. This is joint work with C. Evan Zohar,
N. Linial and T. Nowik.

**Cameron Gordon**, UT Austin

Nov 13th, 2015

**Title**: Taut foliations, left-orderability and cyclic branched coverings

**Abstract**: It is conceivable that for a prime, closed,
orientable 3-manifold the following are equivalent: (1) $M$ admits a
co-orientable taut foliation, (2) $\pi_1(M)$ is left-orderable, and
(3) $M$ is not a Heegaard Floer L-space. We will discuss this in the
case where $M$ is the $n$-fold cyclic branched covering of a
knot. This is joint work with Tye Lidman.

**Christian Zickert**, University of Maryland

Nov 20th, 2015

**Title**: Triangulation independent Ptolemy varieties

**Abstract**: The Ptolemy variety is an invariant of a triangulated
3-manifold M. It detects SL(2,C)-representations of pi_1(M) in the
sense that every point in the Ptolemy variety canonically determines a
representation (up to conjugation). It is closely related to
Thurston's gluing equation variety for
PSL(2,C)-representations. Unfortunately, both the gluing equation
variety and the Ptolemy variety depend on the triangulation and may
miss several components of representations. We discuss the basic
properties of these varieties, how to compute invariants such as trace
fields and complex volume, and how to obtain a variety, which is
independent of the triangulation.

** Andrei Vesnin**, Chelyabinsk, Russia

Dec 4th, 2015

**Title**: Around right-angled hyperbolic polyhedra

**Abstract**: Right-angled polyhedra in hyperbolic spaces are
serving as useful building blocks for constructing hyperbolic
manifolds and orbifolds with interesting properties. We will look at
dimension three, where we describe existence conditions and the volume
set structure. Then we will present a way to construct closed
hyperbolic 3-manifolds related to color-epimorphisms of right-angled
Coxeter groups and find 2-fold branched coverings of the 3-sphere. As
a particular case, we will discuss the first example of a closed
orientable hyperbolic 3-manifold constructed by F. Loebell in 1931.

# Other relevant information.

Spring 2016## Previous semesters:

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.