Seminars and Colloquia by Series

Oral Comprehensive Exam

Series
Geometry Topology Seminar
Time
Monday, April 18, 2011 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Becca WinarskiGeorgia Tech

Please Note: The actual talk will be 40 minutes. Note the unusual time.

The theorem of Birman and Hilden relates the mapping class group of a surface and its image under a covering map. I'll explore when we can extend the original theorem and possible applications for further work.

Generalized Kashaev and Turaev-Viro 3-manifold invariants

Series
Geometry Topology Seminar
Time
Monday, April 11, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Nathan GeerUtah State University
I will consider two constructions which lead to information about the topology of a 3-manifold from one of its triangulation. The first construction is a modification of the Turaev-Viro invariant based on re-normalized 6j-symbols. These re-normalized 6j-symbols satisfy tetrahedral symmetries. The second construction is a generalization of Kashaev's invariant defined in his foundational paper where he first stated the volume conjecture. This generalization is based on symmetrizing 6j-symbols using *charges* developed by W. Neumann, S. Baseilhac, and R. Benedetti. In this talk, I will focus on the example of nilpotent representations of quantized sl(2) at a root of unity. In this example, the two constructions are equal and give rise to a kind of Homotopy Quantum Field Theory. This is joint work with R. Kashaev, B. Patureau and V. Turaev.

The Degree Conjecture for torus knots

Series
Geometry Topology Seminar
Time
Monday, April 4, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Thao VuongGeorgia Tech
I will talk about some progress in proving the Degree Conjecture for torus knots. The conjecture states that the degree of a colored Jones polynomial colored by an irreducible representation of a simple Lie algebra g is locally a quadratic quasi-polynomial. This is joint work with Stavros Garoufalidis.

Skewloops, quadrics, and curvature

Series
Geometry Topology Seminar
Time
Monday, March 14, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Bruce SolomonIndiana University
A smooth loop in 3-space is skew if it has no pair of parallel tangent lines. With M.~Ghomi, we proved some years ago that among surfaces with some positive Gauss curvature (i.e., local convexity) the absence of skewloops characterizes quadrics. The relationship between skewloops and negatively curved surfaces has proven harder to analyze, however. We report some recent progress on that problem, including evidence both for and against the possibility that the absence of skewloops characterizes quadricsamong surfaces with negative curvature.

Contact geometry and Heegaard Floer invariants for noncompact 3-manifolds

Series
Geometry Topology Seminar
Time
Friday, March 11, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Shea Vela-VickColumbia University
I plan to discuss a method for defining Heegaard Floer invariants for 3-manifolds. The construction is inspired by contact geometry and has several interesting immediate applications to the study of tight contact structures on noncompact 3-manifolds. In this talk, I'll focus on one basic examples and indicate how one defines a contact invariant which can be used to give an alternate proof of James Tripp's classification of tight, minimally twisting contact structures on the open solid torus. This is joint work with John B. Etnyre and Rumen Zarev.

On Automorphisms of the Hyperelliptic Torelli Group

Series
Geometry Topology Seminar
Time
Monday, February 28, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Leah ChildersPittsburg State U
We will discuss the structure of the symmetric (or hyperelliptic) Torelli group. More specifically, we will investigatethe group generated by Dehn twists about symmetric separating curvesdenoted by H(S). We will show that Aut(H(S)) is isomorphic to the symmetricmapping class group up to the hyperelliptic involution. We will do this bylooking at the natural action of H(S) on the symmetric separating curvecomplex and by giving an algebraic characterization of Dehn twists aboutsymmetric separating curves.

Spinal Open Books and Symplectic Fillings

Series
Geometry Topology Seminar
Time
Monday, February 21, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jeremy Van Horn-MorrisAIM
A theorem of Chris Wendl allows you to completely characterize symplectic fillings of certain open book decompositions by factorizations of their monodromy into Dehn twists. Olga Plamenevskaya and I use this to generalize results of Eliashberg, McDuff and Lisca to classify the fillings of certain Lens spaces. I'll discuss this and a newer version of Wendl's theorem, joint with Wendl and Sam Lisi, this time for spinal open books, and discuss a few more applications.

Legendrian and transverse knots in cabled knot types

Series
Geometry Topology Seminar
Time
Monday, February 14, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Bulent TosunGa Tech
In this talk we will exhibit many new phenomena in the structure of Legendrian and transverse knots by giving a complete classification of all cables of the positive torus knots. We will also provide two structural theorems to ensure when cable of a Legendrian simple knot type is also Legendrian simple. Part of the results are joint work with John Etnyre and Douglas LaFountain

Hyperbolic polyhedra and the Jones polynomial

Series
Geometry Topology Seminar
Time
Monday, February 7, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Roland van der VeenUCBerkeley
For knots the hyperbolic geometry of the complement is known to be relatedto itsJones polynomial in various ways. We propose to study this relationship morecloselyby extending the Jones polynomial to graphs. For a planar graph we will showhow itsJones polynomial then gives rise to the hyperbolic volume of the polyhedronwhose1-skeleton is the graph. Joint with Francois Gueritaud and FrancoisCostantino.

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