# Joint IAS-PU Symplectic Geometry Seminar

### 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...

### Infinite staircases and reflexive polygons

Ana Rita Pires
A classic result, due to McDuff and Schlenk, asserts that the function that encodes when a four-dimensional symplectic ellipsoid can be embedded into a four-dimensional ball has a remarkable structure: the function has infinitely many corners...

### Distinguishing monotone Lagrangians via holomorphic annuli

We present techniques for constructing families of compact, monotone (including exact) Lagrangians in certain affine varieties, starting with Brieskorn-Pham hypersurfaces. We will focus on dimensions 2 and 3. In particular, we'll explain how to set...

### Floer Cohomology and Arc Spaces

Let f be a polynomial over the complex numbers with an isolated singular point at the origin and let d be a positive integer. To such a polynomial we can assign a variety called the dth contact locus of f. Morally, this corresponds to the space of d...

### Reeb orbits that force topological entropy

Abror Pirnapasov
A transverse link in a contact 3-manifold forces topological entropy if every Reeb flow possessing this link as a set of periodic orbits has positive topological entropy. We will explain how cylindrical contact homology on the complement of...

### Real Lagrangian Tori in toric symplectic manifolds

Joé Brendel
In this talk we will be addressing the question whether a given Lagrangian torus in a toric monotone symplectic manifold can be realized as the fixed point set of an anti-symplectic involution (in which case it is called "real"). In the case of...

### Infinite staircases of symplectic embeddings of ellipsoids into Hirzebruch surfaces

Morgan Weiler
Gromov nonsqueezing tells us that symplectic embeddings are governed by more complex obstructions than volume. In particular, in 2012, McDuff-Schlenk computed the embedding capacity function of the ball, whose value at a is the size of the smallest...

### Duality for Rabinowitz-Floer homology

Alex Oancea
I will explain a duality theorem with products in Rabinowitz-Floer homology. This has a bearing on string topology and explains a number of dualities that have been observed in that setting. Joint work in progress with Kai Cieliebak and Nancy...