The SGGT seminar meets on Fridays in Math 507, from 1:00-2:00, except as noted.

Previous semesters: spring 2007, fall 2006.

Next semester: spring 2008.

Other area seminars. Our e-mail list.

SGGT seminar schedule. (iCal)
Date Speaker Title

Sept. 20 (Thursday), Courant Institute, NYU, Room 613

New York Area Joint Symplectic Geometry Seminar  
4:00 p.m.: Urs Frauenfelder (Munich) On Floer Rabinowitz homology
5:15 p.m.: Leonid Polterovich (Tel Aviv) Floer theory vs. quantum-classical correspondence
Sept. 21 R. Inanc Baykur (Columbia) Finite group actions and exotic smooth structures on 4-manifolds
Sept. 28 No seminar this week.
Oct. 5 Kevin Costello (Northwestern)

Perturbative Chern-Simons theory
Oct. 12 Ciprian Manolescu (Columbia) Symplectic instanton homology
Oct. 19 Isidora Milin (Stanford) Orderability and (Non)Squeezing in Contact Geometry
Oct. 26 Anar Akhmedov (Georgia Tech) Exotic 4-manifolds with small Euler characteristics
Nov. 2 Peter Kronheimer (Harvard) Knot invariants from singular instantons
Nov. 9, 2:15 p.m. Josh Greene (Princeton) Concordance Order and Three-Stranded Pretzel Knots
Nov. 16 Michael Usher (Princeton) Spectral Numbers in Floer theories
Nov. 23 No seminar this week.
Nov. 30 Andrew Cotton-Clay (U. C. Berkeley) Symplectic Floer homology of pseudo-Anosov and reducible maps

Dec. 7, in Math 312, Columbia University

 New York Area Joint Symplectic Geometry Seminar  
4:00 p.m.: Larry Guth (Stanford) Symplectic embeddings of polydisks
5:15 p.m.: Soren Galatius (Stanford) Holomorphic curves and stable homotopy theory

 

Abstracts.

September 20, 2007.

4:00 p.m.: Urs Frauenfelder, "On Floer Rabinowitz homology" (PDF, iCal)

5:15 p.m.: Leonid Polterovich, "Floer theory vs. quantum-classical correspondence" (PDF, iCal)

 

September 21, 2007.

R. Inanc Baykur, "Finite group actions and exotic smooth structures on 4-manifolds" (PDF, iCal)

Abstract: In this talk, I will discuss an equivariant version of the reverse engineering technique of Fintushel and Stern. I will then demonstrate how this technique can be used to produce some new examples of real symplectic 4-manifolds, infinite families of small exotic 4-manifolds, and infinite families of (possibly) exotic embeddings of surfaces. This is work in progress.

 

October 5, 2007.

Kevin Costello, "Perturbative Chern-Simons theory" (PDF, iCal)

Abstract: I'll explain a construction of an algebraic structure on the cohomology of a manifold, which arises by renormalising certain Chern-Simons functional integrals. This algebraic structure seems to be very similar to structures coming from symplectic field theory on the unit cosphere bundle.

 

October 12, 2007.

Ciprian Manolescu, "Symplectic instanton homology" (PDF, iCal)

Abstract: I will present some new invariants of 3-manifolds, one for each simple, simply connected, compact Lie group G different from SU(n). The invariants are constructed using Lagrangian Floer homology, and closely related to the symplectic side of the Atiyah-Floer Conjecture. This is joint work with Chris Woodward.

 

October 19, 2007.

Isidora Milin, "Orderability and (Non)Squeezing in Contact Geometry" (PDF, iCal)

Abstract: We say that a contact isotopy of a contact manifold is "positive"
if during the isotopy each point of the manifold moves in a positively
transverse direction to the contact hyperplane distribution. The question of
whether this notion induces a partial order on the universal cover of the
identity component of the contactomorphism group - whether the contact
manifold is "orderable" - turns out to be sensitive to the topology of the
contact manifold, and is related to nonsqueezing phenomena in contact geometry,
as studied by Eliashberg, Kim and Polterovich.

I will begin by explaining this relation and what we know so far about
the orderability question, and then describe a version of contact homology
for domains that enables us to detect relevant contact nonsqueezings. This
will be illustrated by standard contact sphere (not orderable) and
lens spaces (orderable), and, if time permits, by general prequantization spaces.
Towards the end, I will indicate what the analogue of rotation number for a circle
diffeomorphism might be in this context.

 

October 26, 2007.

Anar Akhmedov, "Exotic 4-manifolds with small Euler characteristics" (PDF, iCal)

Abstract: It is known that many simply connected, smooth topological 4-manifolds admit infinitely many smooth structures. The smaller the Euler characteristic, the
harder it is to construct exotic smooth structure.

In this talk we present new examples of symplectic 4-manifolds with same integral cohomology as S^2 x S^2. We also discuss the generalization of these examples to #_{2n-1}(S^2 x S^2) for n > 1. As an application of these symplectic building blocks, we construct exotic smooth structure on small 4-manifolds such as CP^2#k(-CP^2) for k = 2, 3, 4, 5 and 3CP^2#l(-CP^2) for l=4, 5, 6, 7. We will also discuss an interesting applications to the geography of minimal symplectic 4-manifolds.

Most of this is joint work with B. Doug Park.

 

November 2, 2007.

Peter Kronheimer, "Knot invariants from singular instantons" (PDF, iCal)

 

November 9, 2007, 2:15-3:15 p.m.

Josh Greene, "Concordance Order and Three-Stranded Pretzel Knots" (PDF, iCal)

Abstract: I will talk about two recent approaches to the study of smooth knot concordance, one coming from Donaldson theory, the other from Heegaard Floer homology. Then I will discuss how to combine the two to give an interesting test for a knot to be slice, and apply the test to determine the concordance order of three-stranded pretzel knots.

 

November 16, 2007.

Michael Usher, "Spectral Numbers in Floer theories" (PDF, iCal)

 

November 9, 2007, 2:15-3:15 p.m.

Josh Greene, "Concordance Order and Three-Stranded Pretzel Knots" (PDF, iCal)

Abstract: I will talk about two recent approaches to the study of smooth knot concordance, one coming from Donaldson theory, the other from Heegaard Floer homology. Then I will discuss how to combine the two to give an interesting test for a knot to be slice, and apply the test to determine the concordance order of three-stranded pretzel knots.

 

November 30, 2007.

Andrew Cotton-Clay, "Symplectic Floer homology of pseudo-Anosov and reducible maps" (PDF, iCal)

Abstract: Symplectic Floer homology assigns to a symplectomorphism f a Z/2-graded chain complex generated by the fixed points of f with differentials given by counting holomorphic cylinders in M_f x R, where M_f is the mapping torus of f. The homology HF_*(f) is invariant under certain deformations of f. We show how to calculate HF_*(f) using train tracks for f any surface symplectomorphism in a pseudo-Anosov mapping class as well as for f a reducible symplectomorphism satisfying a certain weak monotonicity condition. In combination with previous work by Seidel, Gautschi, and Eftekhary, this completes the computation of Seidel's HF_*(g) for g any (oriented) mapping class. Our results also include surfaces with boundary.

 

December 7, 2007.

4:00 p.m.: Larry Guth, "Symplectic embeddings of polydisks" (PDF, iCal)

Abstract: We construct some new symplectic embeddings of polydisks. With these embeddings, we can determine - up to a constant factor - whether one
polydisk embeds in another. In the first half of the talk, I will describe the result and some context and corollaries. In the second half of the talk, I will give the main idea of the construction.

5:15 p.m.: Soren Galatius, "Holomorphic curves and stable homotopy theory" (PDF, iCal)

Abstract: Let M(X) denote the moduli space of (nodal, stable, genus g) curves holomorphic curves in X. Invariants (e.g. Gromov-Witten) can be extracted from two ingredients: (Parts of) the cohomology ring H^*(M(X)), and the fundamental class H^*(M(X)) -> Q. I will describe a space F(X) and a natural map u: M(X) -> F(X). From the point of view of stable homotopy theory, the definition of the space F(X) is a rather natural construction, and in particular the rational cohomology ring of F(X) can be easily and explicitly described. All relevant cohomology classes in M(X) arise as pull back from classes in F(X). This framework collects all the "homotopy theoretic" information into one object, and all the "analytic" information is encoded in the fundamental class H^*(F(X)) -> Q. In the case where X is a point (my talk will focus on this case), the fundamental class "is" the power series determined by Kontsevich's theorem (Witten's conjecture). This is joint work with Ya. Eliashberg.

 

Other relevant information.

Other area seminars.

Area conferences.

Sept. 24-28, 2007
CUNY Graduate Center

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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.