Roger Casals (MIT)
Baptiste Chantraine (Nantes)
John Etnyre (Georgia Tech)
Emmy Murphy (MIT)
Lenny Ng (Duke)
Lisa Traynor (Bryn Mawr)
Schedule (all talks to take place in Simonyi Hall 101)
Thursday February 11, 2016
Friday February 12
||Restrictions on the fundamental group of some Lagrangian cobordisms.
||Toward a contact Fukaya category
||Satellite operations and Legendrian knot theory
||A frontal view on Lefschetz fibrations I
||A frontal view on Lefschetz fibrations II
||A Quantitative Look at Lagrangian Cobordisms
Chantraine Abstract: In this talk we will describe two methods which shows
that, under some rigidity assumptions on the involved Legendrian
submanifolds, a Lagrangian cobordism is simply connected. The first one
uses the functoriality of the fundamental class in Legendrian contact
homology with twisted coefficients. The second uses a L^2-completion of
the Floer complex associated to the cobordism. This is joint work with G.
Dimitroglou Rizell, P. Ghiggini and R. Golovko.
Ng Abstract: I will describe some work in progress (maybe more accurately,
wild speculation) regarding a version of the derived Fukaya category for
contact 1-jet spaces J^1(X). This category is built from Legendrian
submanifolds equipped with augmentations, and the full subcategory
corresponding to a fixed Legendrian submanifold \Lambda is the
augmentation category Aug(\Lambda), which I will attempt to review. The
derived Fukaya category is generated by unknots, with the corollary that
all augmentations ``come from unknot fillings''. I will also describe a
potential application to proving that ``augmentations = sheaves''. This is
work in progress with Tobias Ekholm and Vivek Shende, building on joint
work with Dan Rutherford, Vivek Shende, Steven Sivek, and Eric Zaslow.
Etnyre Abstract: Satellite operations are a common way to create
interesting knot types in the smooth category. It starts with a knot K,
called the companion knot, in some manifold M and another knot P, called
the pattern, in S^1\times D^2 and then creates a third knot P(K), called
the satellite knot, as the image of P when S^1\times D^2 is identified
with a neighborhood of K. In this talk we will discuss the relation
between Legendrian knots representing K, P, and P(K). Sometimes the
classification of Legendrian representatives for K and P yields a
classification for P(K), but other times it does not. We will discuss why
this happens and a general framework for studying Legendrian Satellites.
Casals & Murphy Abstract: In this series of two talks we will discuss
Weinstein structures endowed with a Lefschetz fibration in terms of the
Legendrian front projection. The main focus is on Weinstein manifolds
which admit a Weinstein Lefschetz fibration with an $A_k$--fibre; this
provides a large class of Weinstein structures ranging from flexible
Weinstein manifolds to rich rigid examples. In particular, we will
describe the computation of their symplectic homologies and discuss its
implications to Legendrian submanifolds and their Lagrangian fillings.
Traynor Abstract: Lagrangian cobordisms between Legendrian submanifolds
arise in Relative Symplectic Field Theory. In recent years, there has been
much progress on answering qualitative questions such as: For a fixed pair
of Legendrians, does there exist a Lagrangian cobordism? I will address
two quantitative questions about Lagrangian cobordisms: For a fixed pair
of Legendrians, what is the minimal “length” of a Lagrangian cobordism?
What is the relative Gromov width of a Lagrangian cobordism? Regarding
length, I will give examples of pairs of Legendrians where Lagrangian
cobordisms are flexible in that the non-cylindrical region can be
arbitrarily short; I will also give examples of other pairs of Legendrians
where Lagrangian cobordisms are rigid in that there is a positive lower
bound to their length. For the second quantitative measure, I will give
some calculations and estimates of the relative Gromov width of particular
Lagrangian cobordisms. This is joint work with Joshua M. Sabloff.
Sadly we have no funding, however there will be free cookies, tea, and
coffee each day from 3-4pm in Fuld Hall. Additionally, the talks will be
videotaped, with links appearing on this webpage.