# Joint IAS-PU Symplectic Geometry Seminar

### Symplectomorphisms mirror to birational transformations of the complex plane

We construct a non-finite type four-dimensional Liouville manifold MM and describe a correspondence between certain birational transformations of the complex plane preserving a standard holomorphic volume form and symplectomorphisms of MM. This...

### Morse-Bott theory on singular analytic spaces and applications to the topology of symplectic four-manifolds

We describe two extensions, called the virtual Morse-Bott index and circle-equivariant virtual Morse-Bott index, of the classical Morse-Bott index of a Morse-Bott function on a smooth manifold to the setting of (a) suitably defined analytic...

### Legendrian Torus and Cable Links

Legendrian torus knots were classified by Etnyre and Honda. I will explain the classification of Legendrian torus links. In particular, I will describe restrictions on the Legendrian torus knots that can be realized as the components of a Legendrian...

### ECH of prequantization bundles

The 2011 PhD thesis of Farris outlined a scheme to show that the ECH of a prequantization bundle over a Riemann surface is isomorphic as a Z/2Z-graded group to the exterior algebra of the homology of its base. In addition to providing an overview of...

### Lagrangian Cobordisms and Enriched Knot Diagrams

We present some obstructions to the existence of Lagrangian cobordisms in ?4. The obstructions arise from studying moduli spaces of holomorphic disks with corners with boundaries on immersed objects called Lagrangian tangles. The obstructions boil...

### A (slightly deeper) look into the restricted 3-body problem

In this talk, as a continuation of my talk in the Members’ Colloquium but with a specialized audience in mind, I will discuss in more detail some of the general geometric and dynamical structures underlying the theoretical aspects of the restricted...

### Contractibility of the space of tight contact structures on R^3

30 years ago I proved that any tight contact structure on the 3-sphere is diffeomorphic to the standard one. I also optimistically claimed at the same paper that similar methods could be used to prove a multi-parametric version: the space of tight...

### Pontryagin - Thom for orbifold bordism

The classical Pontryagin–Thom isomorphism equates manifold bordism groups with corresponding stable homotopy groups. This construction moreover generalizes to the equivariant context. I will discuss work which establishes a Pontryagin--Thom...

### Homogeneous quasimorphism, C^0-topology and Lagrangian intersection

Yusuke Kawamoto, Shira Tanny, Javier Martínez-Aguinaga
Yusuke Kawamoto: Homogeneous quasimorphism, C^0-topology and Lagrangian intersection Abstract: We construct an example of a non-trivial homogeneous quasimorphism on the group of Hamiltonian diffeomorphisms of the 2- and 4-dimensional quadric...

### Knot Floer homology and bordered algebras

Knot Floer homology is an invariant for knots in three-space, defined as a Lagrangian Floer homology in a symmetric product. It has the form of a bigraded vector space, encoding topological information about the knot. I will discuss an algebraic...