The Informal Symplectic Geometry Seminar meets 9:30-10:30am in Math 417 on Fridays. The Informal Symplectic Geometry Seminar should not be confused with Columbia's more traditional Symplectic Geometry and Gauge Theory seminar.
Previous semesters: Spring 2009, Fall 2008, Spring 2008, Fall 2007.
| Date | Speaker | Title |
|---|---|---|
Sept. 18 |
Peter Horn (Columbia) | Knot concordance and gropes |
Sept. 25 |
Peter Horn (Columbia) | Knot concordance and gropes (continued) |
Oct. 2 |
10:45 a.m.: Michael Brandenbursky (Technion) | Knot theory and quasi-morphisms |
Oct. 9 |
Sabin Cautis (Columbia) | On the symplectic knot homologies of Seidel, Smith and Manolescu |
Oct. 16 |
Sabin Cautis (Columbia) | On the symplectic knot homologies of Seidel, Smith and Manolescu (continued) |
Oct. 23 |
No seminar this week |
|
Oct. 30 |
Josh Greene (Columbia) | Lens space surgeries and genus bounds |
Nov. 6 |
No seminar this week |
|
Nov. 13 |
Sucharit Sarkar (Columbia) | A construction of knot Floer homology |
Nov. 20 |
Evan Fink (Columbia) | Floer homology of mapping tori |
Nov. 27 |
No seminar this week |
|
Dec. 4 |
No seminar this week |
|
Dec. 11 |
No seminar this week |
|
Abstracts.
September 18 and 25, 2009.
Peter Horn (Columbia), "Knot concordance and gropes"
Abstract: In the late 90s, Cochran, Orr and Teichner introduced two filtrations of the knot concordance group. I will discuss the grope filtration of the knot concordance group and some invariants that are generalizations of the slice genus of a knot. I will discuss some of the constructions and obstructions in this corner of knot theory.
October 2, 2009.
Michael Brandenbursky (Technion), "Knot theory and quasi-morphisms"
Abstract (pdf): Quasi-morphisms on a group are real-valued functions which satisfy the homomorphism equation "up to a bounded error". They are known to be a helpful tool in the study of the algebraic structure of non-Abelian groups. I will discuss a construction relating:
a) certain knot and link invariants-in particular, the ones that come from the knot Floer homology and a Khovanov-type homology,
b) braid groups,
c) the dynamics of area-preserving diffeomorphisms of a two dimensional disc,
d) quasi-morphisms on the group of all such compactly supported diffeomorphisms of the disk.
October 9 and 16, 2009.
Sabin Cautis (Columbia), "On the symplectic knot homologies of Seidel, Smith and Manolescu"
Abstract: We survey the symplectic knot homology constructed by Seidel-Smith (and generalized by Manolescu) and compare it to its algebro-geometric counterpart constructed in joint work with Kamnitzer. The two constructions are related by a hyperKahler rotation and the spaces involved are ultimately related to the affine Grassmannian. We will study these spaces in an elementary way.
October 30, 2009.
Josh Greene, "Lens space surgeries and genus bounds"
Abstract: Which lens spaces L(p,q) arise by integer surgery on a knot K in S^3? We will discuss a necessary and conjecturally sufficient condition on the pair (p,q) which is lattice-theoretic in nature. Making use of it, we will derive an inequality relating the knot genus g(K) with the surgery slope p, improving an earlier estimate of Kronheimer-Mrowka-Ozsvath-Szabo and essentially solving a conjecture of Goda-Teragaito.
November 13, 2009.
Sucharit Sarkar, "A construction of knot Floer homology"
Abstract: We will give an overview of how to construct a CW comlpex in a well-defined fashion from a grid diagram, such that the cellular chain complex of the CW comlpex is the grid chain complex. We will describe some of the properties that the CW complex has, and show that the stable homotopy type of the CW complex is a knot invariant.
Other relevant information.
Our e-mail list.
Announcements for this seminar, as well as for related seminars and events, are sent to the "Floer Homology" e-mail list maintained via Google Groups. You can subscribe directly via Google Groups or by contacting R. Lipshitz.