Buffalo Geometry and Topology Seminar

Fall 2009

Unless noted, all seminars are Friday at 4pm, in Mathematics 122.

Date Speaker Organization Title Abstract

September 4th Organizational Meeting

September 11th William Menasco University at Buffalo The "Markov Theorem without Stabilization" after H. Matsuda This will be a discussion of Matsuda's new proof of the MTWS along with an overview of the central ideas of his proof.

September 18th Doug LaFountain University at Buffalo Iterated torus knots that satisfy the uniform thickness property The uniform thickness property (UTP) is a property of knots embedded in the 3-sphere with the standard contact structure, and has been useful in studying the Legendrian and transversal classification of cabled knot types. We show that every iterated torus knot which contains at least one negative iteration in its cabling sequence satisfies the UTP. We also conjecture a complete UTP classification for iterated torus knots, and fibered knots in general.

September 25th William Menasco University at Buffalo "MTWS", part II

October 2nd Eduardo Martínez-Pedroza McMaster University Surface subgroups in some Negatively Curved Groups An outstanding conjecture by M. Gromov asserts that a one-ended hyperbolic group contains a subgroup isomorphic to the fundamental group of a closed surface. Motivated by this conjecture, we study the existence of immersions of closed surfaces in 2-dimensional CW-complex. Our results provide sufficient conditions for the existence of such immersions and imply the existence of surface subgroups in a class of hyperbolic groups arising as fundamental groups of locally CAT(0) complexes. Joint work with N. Brady and M. Forester.

October 9th NO SEMINAR

October 15th (Colloquium) Danny Calegari Caltech Faces of the scl norm ball It often happens that a solution of an extremal problem in geometry has more regularity and nicer features than one has an a priori right to expect. I will show how a simple topological problem - when does an immersed curve on a surface bound an immersed subsurface? - is unexpectedly related to linear programming in nonseparable Banach spaces, and gives rise to geometric and dynamical rigidity and discreteness of symplectic representations.

~~October 16th~~ No seminar

October 23rd

October 30th

November 6th

November 13th Bulent Tosun Georgia Tech On the Legendrian and transverse classification of cabled knot types In 3-dimensional contact topology one of the main problem is classifying Legendrian (transverse) knots in certain knot type up to Legendrian (transverse) isotopy. In particular we want to decide if two (one in the case of transverse knots) classical invariants of this knots are complete set of invariants. If it is, then we call this knot type Legendrian (transversely) simple knot type otherwise it is called Legendrian (transversely) non-simple. In this talk, by tracing the techniques developed by Etnyre and Honda, we will present some results concerning the complete Legendrian and transverse classification of certain cabled knots in the standard tight contact 3-sphere. Moreover we will provide an infinite family of Legendrian and transversely non-simple prime knots.

November 20th Daniel Groves University of Illinois at Chicago Parametrizing surface bundles. Let S be an orientable surface of finite type (not a torus or a sphere) and B a reasonable space (CW complex or manifold). Then the set of S-bundles over B is naturally parametrised by the set Hom(pi_1(B),Mod(S))/~ of conjugacy classes of homomorphisms from the fundamental group of B to the mapping class group of S.
I will discuss some recent work (still being written) which provides a description of this set of homomorphisms whenever pi_1(B) is finitely generated.

December 4th

Old seminar pages:

Spring 2007

Fall 2007

Spring 2008

Fall 2008

Date	Speaker	Organization	Title	Abstract
September 4th	Organizational Meeting
September 11th	William Menasco	University at Buffalo	The "Markov Theorem without Stabilization" after H. Matsuda	This will be a discussion of Matsuda's new proof of the MTWS along with an overview of the central ideas of his proof.
September 18th	Doug LaFountain	University at Buffalo	Iterated torus knots that satisfy the uniform thickness property	The uniform thickness property (UTP) is a property of knots embedded in the 3-sphere with the standard contact structure, and has been useful in studying the Legendrian and transversal classification of cabled knot types. We show that every iterated torus knot which contains at least one negative iteration in its cabling sequence satisfies the UTP. We also conjecture a complete UTP classification for iterated torus knots, and fibered knots in general.
September 25th	William Menasco	University at Buffalo	"MTWS", part II
October 2nd	Eduardo Martínez-Pedroza	McMaster University	Surface subgroups in some Negatively Curved Groups	An outstanding conjecture by M. Gromov asserts that a one-ended hyperbolic group contains a subgroup isomorphic to the fundamental group of a closed surface. Motivated by this conjecture, we study the existence of immersions of closed surfaces in 2-dimensional CW-complex. Our results provide sufficient conditions for the existence of such immersions and imply the existence of surface subgroups in a class of hyperbolic groups arising as fundamental groups of locally CAT(0) complexes. Joint work with N. Brady and M. Forester.
October 9th	NO SEMINAR
October 15th (Colloquium)	Danny Calegari	Caltech	Faces of the scl norm ball	It often happens that a solution of an extremal problem in geometry has more regularity and nicer features than one has an a priori right to expect. I will show how a simple topological problem - when does an immersed curve on a surface bound an immersed subsurface? - is unexpectedly related to linear programming in nonseparable Banach spaces, and gives rise to geometric and dynamical rigidity and discreteness of symplectic representations.
~~October 16th~~	No seminar
October 23rd
October 30th
November 6th
November 13th	Bulent Tosun	Georgia Tech	On the Legendrian and transverse classification of cabled knot types	In 3-dimensional contact topology one of the main problem is classifying Legendrian (transverse) knots in certain knot type up to Legendrian (transverse) isotopy. In particular we want to decide if two (one in the case of transverse knots) classical invariants of this knots are complete set of invariants. If it is, then we call this knot type Legendrian (transversely) simple knot type otherwise it is called Legendrian (transversely) non-simple. In this talk, by tracing the techniques developed by Etnyre and Honda, we will present some results concerning the complete Legendrian and transverse classification of certain cabled knots in the standard tight contact 3-sphere. Moreover we will provide an infinite family of Legendrian and transversely non-simple prime knots.
November 20th	Daniel Groves	University of Illinois at Chicago	Parametrizing surface bundles.	Let S be an orientable surface of finite type (not a torus or a sphere) and B a reasonable space (CW complex or manifold). Then the set of S-bundles over B is naturally parametrised by the set Hom(pi_1(B),Mod(S))/~ of conjugacy classes of homomorphisms from the fundamental group of B to the mapping class group of S. I will discuss some recent work (still being written) which provides a description of this set of homomorphisms whenever pi_1(B) is finitely generated.
December 4th