The SGGTC seminar meets on Fridays in Math 520, at 10:45 am unless noted otherwise (in red).

Previous semesters: Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007.

Other area seminars and conferences. Our e-mail list.

# Abstracts

#### January 27, 2012 at 10:45 am

Michael Huthcings, "New symplectic embedding obstructions in four dimensions"

**Abstract:** After reviewing some background on symplectic embedding problems, I will describe some recently
discovered obstructions to symplectically embedding one symplectic four-manifold (possibly disconnected, usually with
boundary) into another. The obstructions are defined using embedded contact homology (ECH) of contact three-manifolds.
For some interesting symplectic embedding problems which have been solved by Biran and McDuff, the ECH obstructions
turn out to be sharp.

#### February 17, 2012 at 10:45 am

Katrin Wehrheim, "The PSS morphism for general symplectic manifolds"

**Abstract:** In joint work with Peter Albers and Joel Fish we study the
[Piunikhin-Salamon-Schwarz]-map from Morse homology to Floer homology.
For semi-positive symplectic manifolds it is given by counting
pseudoholomorphic spheres with one cylindrical end and one marked
point evaluating to a Morse trajectory space, and its inverse is given
by reversing direction on the Floer end and Morse trajectory.
We extend these definitions to morphisms PSS:HM-->HF and SSP: HF-->HM
on general compact symplectic manifolds, using abstract transversality
results in a polyfold description of the moduli spaces. Cobordism and
grading arguments then prove that the composition of SSP with PSS is
an isomorphism on Morse homology with Novikov coefficients; while
there is no such cobordism for the reversed composition. However, this
suffices to reprove the Arnold conjecture, bounding the number of
Hamiltonian orbits below by the total rank of homology; which was
previously proven by virtual moduli cycle techniques. Moreover, this
could be combined with a spectral sequence argument to see that PSS is
indeed an isomorphism.

#### February 24, 2012 at 10:45 am

Alexandru Oancea, "S^1-equivariant symplectic homology and linearized contact homology"

**Abstract:** The boundary part of S^1-equivariant symplectic homology of
a Liouville domain is isomorphic, using rational coefficients, to
linearized contact homology of the boundary. Applications on the
contact homology side include a rigorous definition that solves
transversality issues, a subcritical surgery long exact sequence, and
the computation of linearized contact homology for unit cosphere
bundles. On the symplectic homology side, applications include the
definition of new algebraic operations. Joint work with F. Bourgeois.

#### March 2, 2012 at 10:45 am

Paul Kirk, "Geography of symplectic 4-manifolds with prescribed fundamental group"

**Abstract:** I'll discuss results on constructing closed 4 manifolds with prescribed
> fundamental group efficiently, especially the case of symplectic 4-manifolds.

#### March 9, 2012 at 10:45 am

Emmanuel Ophstein, "Effective symplectic embeddings"

**Abstract:** I will explain the role played by Liouville forms and symplectic polarizations in the problems of embeddings.
One of the aim is to give an effective version of Lalonde-McDuff's inflation method in the context of symplectic embeddings.
I will try to discuss as many applications as I can among : full packings of symplectic manifolds by ellipsoids, or more general shapes,
explicit maximal ball packings of P^2, or natural neighbourhoods of symplectic curves (in dimension 4).

#### March 23, 2012 at 10:45 am

Vera Vertesi, "Transverse positive braid satellites"

**Abstract:** Classification of transverse knots has been long investigated, and several invariants were defined for their distinction.
One classical invariant is the self-linking number of the transverse knot, that can be given as the linking of the knot with its push off by a
vectorfield in the contact planes that has a nonzero extension over a Seifert surface. Smooth knot types whose transverse representatives are
classified by this classical invariant are called transversaly simple. In this talk I will talk I will prove transverse simplicity is inherited
for positive braid satelites of some smooth knot types.

#### March 30, 2012 at 10:45 am

Shelly Harvey, "Combinatorial Spatial Graph Floer Homology"

**Abstract:** A spatial graph is an embedding, f, of a graph G into S^3.
For each flat, balanced and oriented spatial graph, f(G), we define a
combinatorial invariant HFG(f(G)) which is a bi-graded module over a
polynomial ring in E +V variables, where V is the number of vertices
and E is the number of edges in the graph. This invariant is a
generalization of combinatorial link Floer homology defined by
Manolescu, Ozsvath, Sarkar (MOS) for links in S^3. To do this, we
define a grid diagram for a spatial graph and show that every
embedding can be put into grid form. Following MOS, our invariant is
the homology of a chain complex that counts certain rectangles in the
grid. Although the chain complex depends on the choice of grid, the
homology depends only on the embedding. This is joint work with
Danielle O'Donnol (Smith College).

#### April 6, 2012 at 9:30 am and 10:45 am

Eli Grigsby and Stephan Wehrli, "A relationship between Khovanov-type and Heegaard-Floer-type braid invariants I and II"

**Abstract:** Given a braid, one can associate to it a sequence of "categorified" braid invariants (one for each integer in a finite range) in
two apparently different ways: "algebraically," via the higher representation theory of U_q(sl_2) (using work of Khovanov-Seidel, Chen-Khovanov, and
Brundan-Stroppel), and "geometrically," using the bordered Floer invariants of its double-branched cover (defined by Lipshitz-Ozsvath-Thurston and
reinterpreted by Auroux). In this two-part talk, we will describe what we know so far about the connection between these invariants, focusing on
the relationship between the representation theory and the Floer theory.

The first part of the talk should be accessible to a "general" audience of
topologists, and the second part will give more details about the constructions and the proofs. This is joint work with Denis Auroux.

#### April 13, 2012 at 9:30 am

Igor Kriz, "Field theories, homotopy realizations and Khovanov homology"

**Abstract:** I will talk about joint work with Po Hu and Daniel Kriz on
realizations of 1+1-field theories valued in categories in modules
over rigid ring spectra in stable homotopy theory. As an application,
I will discuss an alternate approach to a recent result of Robert
Lipshitz and Sucharit Sarkar constructing a stable homotopy
refinement of Khovanov homology, and some related topics.

#### April 13, 2012 at 10:45 am

Eduardo Gonzalez, "Seidel Elements and Mirror Transformations"

**Abstract:** Let $X$ be a non-singular projective toric variety whose
anti-canonical class is semipositive (nef). I will present work with
Hiroshi Iritani regarding the relation of Givental's mirror symmetry
transformations with Seidel's invertible elements in the Quantum
Cohomology of $X$. If time permits I will describe a conjecture due to
Chan-Lau-Leung-Tseng that relate this work to lagrangian Floer theory
superpotentials introduced by Fukaya-Ohta-Ono-Oh.

#### April 20, 2012 at 9:30 am

Ciprian Manolescu, "The Heegaard Floer invariant of the circle"

**Abstract:** As part of the bordered Floer homology package, Lipshitz, Ozsvath and D. Thurston have associated to a parametrized oriented
surface a certain differential graded algebra. I will describe a decomposition theorem for this algebra, corresponding to cutting the surface along a
circle. In this decomposition, we associate to the circle a categorical structure called the nilCoxeter sequential 2-algebra. I will also discuss a
decomposition theorem for bordered modules associated to nice diagrams, corresponding to cutting a 3-manifold with boundary along a surface transverse
to the boundary. This is joint work with Christopher Douglas.

#### April 20, 2012 at 10:45 am

Garrett Alston, "Real Lagrangians in the quintic"

**Abstract:** I will talk about some computations of Floer cohomology of real
Lagrangians in the quintic, and I'll relate these computations to matrix
factorizations in the mirror of the quintic. I'll also make some remarks
about the possibility of the real Lagrangians generating the Fukaya
category. This is work in progress.

#### April 27, 2012 at 9:30 am

Jo Nelson, "Cylindrical contact homology as a well-defined homology theory?"

**Abstract:** Symplectic field theory has been around for more than a decade but significant analytic obstacles remain and very few rigorous proofs have appeared in the literature. Cylindrical contact homology is one of the "simplest" invariants coming from this framework, but even the full details of its construction have not been lovingly worked out. In fact it has recently come to light that the usual assumptions on the Conley-Zehnder indices of contractible closed Reeb orbits do not ensure d^2=0 due to the existence of multiply covered cylinders and their branched covers. In this talk I will explain these issues with concrete examples and explore what stronger conditions are necessary on the growth rates of the indices of simple contractible orbits to obtain a homological invariant. I will also sketch a method in progress that seems to avoid these issues for prequantization spaces and certain S^1 bundles over nicely behaved symplectic orbifolds.

#### April 27, 2012 at 10:45 am

Cotton Seed, "Twisting Szabo's geometric spectral sequence"

**Abstract:** Recently, by studying suitably twisted complexes, a number
of knot homology theories have been formulated in terms of complexes
generated by the spanning trees of a knot. In this talk, I will
describe a twisted version of Szabo's geometric spectral sequence in
Khovanov homology. To begin, I will review related constructions:
Roberts' totally twisted Khovanov homology, a twisted variant of the
spectral sequence from Khovanov homology to the double-branched cover,
and Szabo's geometric spectral sequence. I will present my
construction and give some computational results. Finally, I will
describe some natural directions for future work.

#### May 4, 2012

Andras Stipsicz, "Knots in Lattice homology"

**Abstract:** In 2008 Nemethi introduced an invariant of negative definite plumbings, called lattice homology. We introduce a filtration on the
lattice homology of a negative definite plumbing tree associated to a further vertex and show how to determine lattice homologies of surgeries on this
last vertex. We discuss the relation with Heegaard Floer homology.

# Other relevant information

## Conferences

**Interactions Between Algebra and Dynamics in Symplectic Topology**

Technion

June 17 – 21, 2012

**CAST Summer School and Conference**

Alfred Renyi Institute

July 9 – 20, 2012

**Workshop on Symplectic Field Theory VI**

Ludwig-Maximilians-Universitat Munchen

July 23 – 27, 2012

**Workshop and Conference on Holomorphic Curves and Low Dimensional Topology**

Stanford University

Jul 30 – Aug 11, 2012

## Other area seminars

- Columbia Geometric Topology Seminar
- Columbia Algebraic Geometry Seminar
- Eilenberg lecture series
- Princeton Topology Seminar

## 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.