[09:30-10:30] Çağatay Kutluhan,
University at Buffalo,
A Heegaard Floer analog of algebraic torsion
I will talk about joint work in progress with Gordana
Matic, Jeremy Van Horn-Morris, and Andy Wand the goal of which
is to define a Heegaard Floer analog of Latschev and Wendl's
algebraic torsion for contact 3-manifolds. (Notes)
[10:30-11:00] Coffee
[11:00-12:00] John Baldwin, Boston College,
Lagrangian concordance and contact
invariants in sutured Floer theories
In 2007, Honda, Kazez, and Matic defined an invariant of
contact 3-manifolds with convex boundaries using sutured
Heegaard Floer homology (SHF). Last year, Steven Sivek and I
defined an analogous contact invariant using sutured Monopole
Floer homology (SMF). In this talk, I will describe work with
Sivek to prove that these two contact invariants are
identified by an isomorphism relating the two sutured
theories. This has several interesting consequences. First, it
gives a proof of invariance for the contact invariant in SHF
which does not rely on the relative Giroux correspondence
between contact structures and open books (something whose
proof has not yet been written down in full). Second, it gives
a proof that the combinatorially computable invariants of
Legendrian knots in Heegaard Floer homology can obstruct
Lagrangian concordance.
[14:15-15:15] Yi Ni, California Institute of Technology,
Fintushel--Stern knot surgery in torus bundles
Suppose that X is a torus bundle over a closed surface
with homologically essential fibers. Let X_K be the manifold
obtained by Fintushel--Stern knot surgery on a fiber using a
knot K\subset S^3. We prove that X_K has a symplectic
structure if and only if K is a fibered knot.
[15:15-16:00] Tea
[16:00-17:00] Daniel Ruberman, Brandeis University,
Absolutely exotic 4-manifolds
We show the existence of exotic smooth structures on
contractible 4-manifolds. These structures are absolute, in
the sense that they do not depend on a specific marking of the
boundary. This is in contrast to the phenomenon of corks,
which are exotic relative to an automorphism of their
boundaries. The technique is to modify a relatively exotic
manifold to give an exotic one for which we have a good
understanding of the automorphism group of the boundary. This
is joint work with Selman Akbulut.
Tuesday, June 16
[09:30-10:30] John Etnyre, Georgia Institute of Technology,
Braiding and transverse knotting in Euclidean 5-space
It is a well-known result of Hirsch that all 3-manifolds
embed in R^5. It was recently observed by Kasuya that if a
contact 3-manifold embeds in the standard contact structure on
R^5 then its first Chern class must be zero. In this talk I
will discuss joint work with Ryo Furukawa aimed at using
braiding techniques to try to prove the converse and more
generally study contact embedding in R^5. Contact embedding
should be consider the higher dimensional analog of transverse
knot theory. Braided embeddings give an explicit way to
represent some (maybe all) smooth embeddings and should be
useful in computing various invariants. In particular, if time
permits I will discuss a generalization of (transverse) knot
contact homology to this setting and how braided embeddings
might aid in its computation.
[10:30-11:00] Coffee
[11:00-12:00] Olga Plamenevskaya, Stonybrook University,
On right-veering transverse knots
I will discuss some properties of right-veering braids
and relation to transverse invariants.
[14:15-15:15] Lucas Culler, Princeton University,
Integrable systems in Donaldson/Floer theory
I will give examples of families of Abelian varieties
that arise in 4-dimensional gauge theory (Donaldson and
Seiberg-Witten theory). I will then show how a Floer
homology theory satisfying certain formal properties can be
used to construct such a family.
[15:15-16:00] Tea
[16:00-17:00] Dylan Thurston, Indiana University,
Extremal length and degenerations of complex
structures
The construction of Heegaard Floer homology depends on a
complex structure on a Heegaard surface, which is not
combinatorial. If we want to make it more combinatorial, we
may consider degenerating the complex structure. Here, we will
look at one point of view on degenerating complex structures,
in terms of extremal lengths. In particular, extremal lengths
can characterize one complex surface with boundary embeds
inside another, in a way that extends nicely to certain
degenerate limits.
Wednesday, June 17
[09:30-10:30] Elisenda Grigsby, Boston College,
(Sutured) Khovanov homology and
representation theory
I'll describe some of the representation theory
underlying sutured annular Khovanov homology, a variant of
Khovanov homology particularly well-suited to studying links
as braid closures. I'll also say a few words about potential
applications. Warning: this talk contains more questions than
answers. Some of what I'll discuss is joint work with Tony
Licata and Stephan Wehrli, and some is joint work in progress
with Tony Licata.
[10:30-11:00] Coffee
[11:00-12:00] Jen Hom, Columbia University,
Knot Floer homology and concordance
We will discuss applications of knot Floer homology to
concordance. In particular, we will compare the four-ball
genus and concordance genus bounds given by epsilon,
Upsilon(t), tau, and nu-plus, which are all concordance
invariants associated to the knot Floer complex. Parts of this
talk are joint work with Zhongtao Wu.
[14:15-15:15] Matthew Hedden, Michigan State University,
Functoriality of Khovanov-Floer theories
There is now a zoo of spectral sequences from Khovanov
homology to various (often Floer type) homological invariants
of links. In most of these situations, the Floer theory is
known to possess some level of functoriality with respect to
link cobordisms, and Khovanov homology is also known to have
this structure. Given that the E_2 and E_infinty pages of the
spectral sequences are functorial, it is natural to wonder if
all the pages enjoy this structure. I'll formalize a notion
of a "Khovanov-Floer theory", which is a relatively weak set
of axioms placed on a mechanism for assigning filtered
complexes to link diagrams. I'll then discuss how to prove
that all the pages of the resulting spectral sequences are
functorial, and why all the spectral sequences we known of fit
into this framework (and are therefore functorial). This is
joint work with John Baldwin and Andrew Lobb.
[15:15-16:00] Tea
[16:00-17:00] Aliakbar Daemi, Simons Center for Geometry and Physics,
Involutions, Floer Homology, and Surgery Cube
There are various exact triangles for Floer homological
invariants of 3-manifolds (respectively, links) that relate
the invariants of different surgeries (respectively,
resolutions) of a 3-manifold (respectively, link). In some
instances of these invariants, there is a group action that
acts naturally on the ingredients of the theory and hence one
can hope to develop an equivariant Floer thoery. In this talk,
I will discuss the interaction of these group actions with the
exact triangles and its applications in the special case of an
invariant that is defiend in the framework of Yang-Mils gauge
theory.
Thursday, June 18
[09:30-10:30] Kristen Hendricks, University of California at Los Angeles,
Involutive Heegaard Floer homology
In joint work in progress with C. Manolescu, we use the
conjugation symmetry on the Heegaard Floer complexes to define
a three-manifold invariant called involutive Heegaard Floer
homology, which is meant to correspond to Z_4-equivariant
Seiberg-Witten Floer homology. From this we obtain two new
invariants of homology cobordism, explicitly computable for
surgeries on L-space knots and quasi-alternating knots, and
two new concordance invariants of knots, one of which (unlike
other invariants arising from Heegaard Floer homology) detects
non-sliceness of the figure-eight knot.
[10:30-11:00] Coffee
[11:00-12:00] Tye Lidman, University of Texas at Austin,
Knot contact homology detects torus knots
Knot contact homology is an invariant of knots arising
from constructions in contact topology which may in fact be a
complete invariant. Using a description of knot contact
homology in terms of the knot group due to
Cieliebak-Ekholm-Latschev-Ng, we prove that the degree zero
piece of knot contact homology detects every torus
knot.
[14:15-15:15] Bohua Zhan, Massachusetts Institute of Technology,
Combinatorial constructions of Heegaard
Floer homology using bordered invariants
Heegaard Floer homology, for a closed 3-manifold Y, is
usually defined by counting certain holomorphic disks or
curves, in a symplectic manifold coming from a Heegaard
decomposition of Y. Recent developments in bordered Heegaard
Floer theory makes it possible to describe the hat version,
HF^(Y), in terms of purely combinatorial and algebraic
constructions. This works by cutting Y along dividing
surfaces into sufficiently simple pieces, then combining the
bordered invariants of each resulting piece, in a way
similar in spirit to a (2+1)-dimensional topological quantum
field theory. I will give an overview of bordered Floer
theory and then discuss my work in using it to give
combinatorial constructions.
[15:15-16:00] Tea
[16:00-17:00] Zoltán Szabó, Princeton University,
Algebraic methods in knot Floer homology
Friday, June 19
[09:00-10:00] Robert Lipshitz, Columbia University,
Remarks on equivariant Floer homology
Recently, equivariant Floer homology has been used to
construct a number of spectral sequences in Heegaard Floer
homology and symplectic Khovanov homology. In this talk, we
will give a (slightly) new construction of equivariant Floer
homology and use it to tie up a number of loose ends related
to these spectral sequences, addressing questions of
invariance, computability, and when different sequences
agree. This is joint work with Kristen Hendricks and
Sucharit Sarkar.
[10:00-10:15] Coffee
[10:15-11:15] Josh Greene, Boston College,
Definite surfaces and alternating links
I will describe a characterization of alternating links
in terms intrinsic to the link complement and use it to give
new proofs of some of Tait’s conjectures.