Place and Time:
Pretalk: Thursdays 1:00pm – 1:50pm in Lunt 105 (aimed at graduate students)
Research talk: Thursdays 4:10pm – 5:00pm in Lunt 107
Organizers: Bahar Acu and Ezra Getzler
January 24, 2019
- Speaker: Kyler Siegel (Columbia)
- Pretalk title: Introduction to symplectic embedding problems and symplectic capacities
- Abstract: A basic problem in symplectic geometry is to determine what types of symplectic embeddings are possible. The first nontrivial result is Gromov’s celebrated nonsqueezing theorem, which puts fundamental constraints on symplectic transformations beyond volume considerations. Since then, various finer obstructions have been discovered and formalized into the notion of a symplectic capacity. In this talk I will discuss some toy problems (still largely open), survey key results, and highlight the significance of Floer homology and symplectic field theory.
- Research talk at 3pm in room Lunt 105 (Note the unusual time and room.)
- Title: Higher symplectic capacities
- Abstract: I will describe a new family of symplectic capacities based on the equivariant L-infinity structure on symplectic cohomology. These give state of the art obstructions for certain embedding problems such as one symplectic ellipsoid into another. Using symplectic field theory, these capacities can be interpreted in terms of holomorphic curves with tangency constraints. I will also give some structural results which are useful for computations.
February 7, 2019
- Speaker: Emmy Murphy (Northwestern)
- Pretalk title: Weinstein manifolds and wrapped Fukaya categories
- Abstract: We discuss the basic geometry of Weinstein manifolds, particularly their relationship with contact geometry, complex geometry, and handlebody theory. We will also discuss the wrapped Fukaya category, a powerful algebraic object associated to any Weinstein manifold. Besides the basic definition and properties, we will also discuss the essential generation results, and surgery formulas relating it to Legendrian contact homology.
- Research talk
- Title: Inductively collapsing wrapped Fukaya categories and flexibility
- Abstract: A Weinstein manifold is an exact symplectic manifold which has a Lagrangian skeleton: this includes all cotangent bundles and all smooth affine varieties. Associated to any Weinstein manifold is the wrapped Fukaya category of that manifold, an algebraic invariant of the manifold. An important example is that the wrapped category of C^n is trivial. We discuss a partial converse to this statement. This will take us through the worlds of arboreal singularities, partially wrapped categories of Weinstein sectors, and Legendrian h-principles.
February 14, 2019
- Speaker: Sara Venkatesh (IAS)
- Pretalk title: Hamiltonian Floer theory and symplectic cohomology
- Abstract: Starting with closed symplectic manifolds, we introduce Hamiltonian Floer homology and discuss the dynamical information it encodes. We then translate this story to open symplectic manifolds, on which symplectic cohomology is defined.
- Research talk
- Title: Symplectic cohomology of subdomains
- Abstract: Mirror symmetry predicts the existence of Floer invariants that yield “local” information. Guided by this, we construct a quantitative symplectic cohomology theory that detects Floer-essential Lagrangians within subdomains. We illustrate the quantitative behavior of this theory by examining negative line bundles over toric symplectic manifolds.
February 21, 2019
- Speaker: Oleg Lazarev (Columbia)
- Pretalk title: Flexibility and rigidity for Weinstein domains
- Abstract: Weinstein domains are the symplectic analogs of smooth handle-bodies and can be understood explicitly via Legendrian knot theory. I will give examples of Weinstein domains, discuss recent flexibility results, including the high dimensional existence theorem, and give an overview of wrapped Fukaya category, an algebraic invariant built using Lagrangians and J-holomorphic curves.
- Research talk
- Title: Weinstein presentations and K-theory
- Abstract: Weinstein domains are the symplectic analogs of smooth handle-bodies and their presentations can be modified by handle-slides and handle creation/cancellation as in the smooth setting. I will show how to construct minimal presentations for Weinstein domains and give examples of different Legendrian knots producing the same Weinstein domain. I will also explain how these presentations are related to the algebra of the wrapped Fukaya category and its Grothendieck group. In particular, the rank of the Grothendieck group is bounded by the rank of singular cohomology and there is a symplectic interpretation of a theorem of Thomason about subgroups of the Grothendieck group and split-generating subcategories.
March 7, 2019
- Speaker: Baptiste Chantraine (Nantes)
- Pretalk title: Front projections and Lagrangian cobordisms
- Abstract: I will explain how we can use front projections to represent some cobordisms between Legendrian submanifolds. This will allow use to describe cobordisms associated to Lagrangian surgeries and we will see why this type of cobordisms are a priori not symmetric.
- Research talk at 3pm in room Lunt 105 (Note the unusual time and room.)
- Title: Lagrangian cobordisms between Legendrian submanifolds and Lagrangian surgeries
- Abstract: In this talk I will study Lagrangian cobordisms between Legendrian submanifolds arising from some Lagrangian surgeries. From the Floer theory of those cobordisms we can deduce some geometrical descriptions of certain iterated cones in the Fukaya category. I will then explain how those considerations lead to a proof of the fact that Lagrangian cocores generates the wrapped Fukaya category of a Weinstein manifold. This is joint work with G. Dimitroglou Rizell, P. Ghiggini and R. Golovko.