The Informal Heegaard Floer Seminar (formerly the Informal Symplectic Geometry Seminar) meets on Fridays in Math 417 from 9:30 to 10:30.
The Informal Symplectic Geometry Seminar should not be confused with Columbia's more traditional Symplectic Geometry, Gauge Theory and Categorification seminar, which meets Fridays at 10:45 in Math 417.
Previous semesters: Spring 2010, Fall 2010, Spring 2009, Fall 2008, Spring 2008, Fall 2007.
| Date | Speaker | Title |
|---|---|---|
Sept. 9 |
Organizational meeting (after the GT and SGGTC organizational meetings) | |
| Sept. 16 | No seminar this week. | |
| Sept. 23 | Krzysztof Putyra | Odd Khovanov Homology |
| Sept. 30 | Alex Ellis | Odd Symmetric Functions |
| Oct. 7 | Alex Ellis | Odd Symmetric Functions, part 2. |
| Oct. 14 | No seminar this week. | |
| Oct. 21 | No seminar this week: SGGTC seminar instead. | |
| Oct. 28 | Krzysztof Putyra | Odd Hn rings and odd Khovanov homology for tangles |
| Nov. 4 | No seminar this week: GT seminar instead. | |
| Nov. 11 | Steven Sivek | Introduction to Monopole Floer Homology |
| Nov. 18 | Rumen Zarev | Overview of bordered Heegaard Floer invariants |
| Nov. 25 | No seminar this week. | |
| Dec. 2 | Maksim Lipyanskiy | Gromov-Uhlenbeck Compactness and the Donaldson-Fukaya Category |
| Dec. 9 | No seminar this week. | |
Abstracts.
September 23, 2011. Krzysztof Putyra, "Odd Khovanov Homology"
Abstract: I will describe a version of Khovanov homology introduced by P. Ozsváth, J. Rasmussen and Z. Szabó. They modified Khovanov's TQFT obtaining a functor defined up to a sign (a projective TQFT) that leads to a chain complex with different homology groups. In my talk I will sketch the construction emphasing both similarities and differences with Khovanov's construction. Then I will extend it to tangles and speculate how it may be related to Reshetikhin-Turaev story.
September 30, 2011. Alexander Ellis, "Odd Symmetric Functions"
Abstract: The odd symmetric functions form a Z-graded Hopf superalgebra which exhibits signed analogues of many of the combinatorial properties of the classical symmetric functions, despite being non-commutative and non-cocommutative. I will review the classical and the odd combinatorics, as well as perhaps the connection with the quantum quasi-symmetric functions of Thibon and Ung. I will also explain how the odd symmetric functions arise in the odd categorification of quantum groups and, conjecturally, odd Khovanov homology. Joint with Mikhail Khovanov and Aaron Lauda.
October 28, 2011. Krzysztof Putyra, "Odd Hn rings and odd Khovanov homology for tangles"
Abstract: For every 2n points on a line we can consider an algebra generated by pictures given by two crossingless matching: one above the line and the other below. A Khovanov functor applied to this algebra produces a ring denoted by Hn. Those rings can be used to define even sl2 homology for tangles.
I will start the talk with this construction and then translate it into the odd framework. The first problem we have to deal with is that the odd variants of Hn rings are no longer commutative. I will show how to overcome this problem using associators and quasi-algebras. This is a joint project with Alexander Shumakovich from GWU.
November 18, 2011. Rumen Zarev, "Overview of bordered Heegaard Floer inariants"
Abstract: I will describe the algebraic structure of Heegaard Floer homology with a view on the bordered theory. If there is enough time I'll say some of the actual definitions.
December 2, 2011. Maksim Lipyanskiy, "Gromov-Uhlenbeck Compactness and the Donaldson-Fukaya Category"
Abstract: We will describe an framework that unites the analysis of the ASD equation with that of holomorphic curves. As an application, we will describe our approach to a version of the Atiyah-Floer conjecture and its categorical generalizations.
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.