The Informal Symplectic Geometry Seminar meets in Math 520 from 3:45 to 5:00 on Fridays. The Informal Symplectic Geometry Seminar should not be confused with Columbia's more traditional Symplectic Geometry and Gauge Theory seminar.
This semester, one focus of the ISGS will be as a reading seminar on the work of Nadler and Zaslow on the relation between the Fukaya category and constructible sheaves; see arXiv:math/0604379v4. Talks in this series are marked with asterisks.
|Robert Lipshitz*||An introduction to the Fukaya category|
|Feb. 6||No seminar this week|
Feb. 12 (Thursday), 1:10-2:40
|Robert Lipshitz and Maksim Lipyanskiy*||More Fukaya category basics; compactness in T*M|
|Feb. 20||No seminar this week: go to the discrete math seminar instead.|
|Feb. 27||No seminar this week.|
March 5 (Thursday), 1:10-2:40
|Joseph Johns*||An introduction to the category of constructible sheaves|
|March 13||Matthew Hedden||New topologically slice knots|
|March 27||Joseph Johns*||Constructible sheaves, part 2.|
|April 3||No seminar this week (probably)|
|Chiu-Chu Melissa Liu*||The Fukaya-Nadler-Zaslow category and microlocalization (I)|
|April 17||No seminar this week: SGGT seminar instead.|
|April 24||Chiu-Chu Melissa Liu*||The Fukaya-Nadler-Zaslow category and microlocalization (II)|
|May 1||No semianr this week: Joint Symplectic Geometry Seminar instead.|
|May 8||Chiu-Chu Melissa Liu*||Nadler's quasi-inverse to the microlocalization functor|
Robert Lipshitz, "An introduction to the Fukaya category."
Abstract: After a gentle introduction to the Fukaya category of a symplectic manifold we will discuss some of the details. In particular, we will discuss coherent perturbations, following the treatment in Seidel's book.
Robert Lipshitz and Maksim Lipyanskiy, "More Fukaya category basics; compactness in T*M."
Abstract: First, RL will introduce "brane structures" (gradings and orientations), and discuss standard Lagrangians in the cotangent bundle. Then ML will discuss how Nadler-Zaslow achieve compactness for moduli spaces of holomorphic curves in T*M.
Matthew Hedden, "New topologically slice knots."
Abstract: A famous theorem of Freedman tells us that a knot with Alexander polynomial one is topologically slice. It could have been the case that these were essentially all the topologically slice knots, in the sense that perhaps any topologically slice knot is smoothly concordant to an Alexander polynomial one knot. I will show that this is not the case - there are topologically slice knots which are not smoothly concordant to any knot with Alexander polynomial one. This indicates that the real *topological* obstruction to sliceness is more complicated than just the polynomial one condition (as one might expect, especially in light of results of Teichner and Friedl). The proof makes use of a formula for the Floer homology of Whitehead doubles, which I will also discuss. This is joint work with Chuck Livingston.
Other relevant information.
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.