CAST 2019 - Program

All talks will take place in Room 2094 at Humboldt University's Hauptgebäude (Main Building), located at Unter den Linden 6. See the practical information page for more details.

Special note about Friday, March 8: The government of the city of Berlin recently proclaimed March 8 as an official public holiday, so almost all stores and public buildings will be closed. The front entrance of the Main Building will also be locked(!) on that day, but the building will be open and accessible from the back via Dorotheenstraße, through the courtyard.

• Thursday, March 7, 2019
  • 13:30 - 14:00: registration
  • 14:00 - 15:00: Peter Albers: Introducing symplectic billiards
  • 15:20 - 16:20: Alexander Fauck: On manifolds with infinitely many fillable contact structures
    coffee break
  • 17:00 - 18:00: Gleb Smirnov: Lagrangian spheres in del Pezzo surfaces
• Friday, March 8, 2019
  • 9:30 - 10:30: Mads Bisgaard: Symplectic Mather theory
    coffee break
  • 11:00 - 12:00: Stefan Nemirovski: Interval topology in contact geometry
    lunch
  • 14:00 - 15:00: Jaime Bustillo: A coisotropic non-squeezing theorem in symplectic geometry
  • 15:20 - 16:20: Pazit Haim-Kislev: The EHZ capacity of convex polytopes
    coffee break
  • 17:00 - 18:00: Ivan Smith: Spherical objects on surfaces
• Saturday, March 9, 2019
  • 9:15 - 10:15: Cheuk Yu Mak: Tropically constructed Lagrangians in mirror quintic threefolds
  • 10:30 - 11:30: Yang Huang: Convex hypersurface theory in higher-dimensional contact topology
    coffee break
  • 12:00 - 13:00: Dusa McDuff: The stabilized symplectic embedding problem

• Peter Albers: Introducing symplectic billiards
  Abstract:
  In the same way "usual" billiards have length as a generating function, symplectic billiards have symplectic area as a generating function. I will explain first in dimension 2 and then in arbitrary dimensions the resulting dynamics and explore its properties. A continuum limit leads to a generalization to a coupled Reeb flow equation. This is joint work with Sergei Tabachnikov.
  
  
• Mads Bisgaard: Symplectic Mather theory
  Abstract:
  I will discuss two different approaches to systematically study invariant sets of Hamiltonian systems. Parts of the first approach builds on results due to Viterbo and Vichery. I will discuss how an analogue of Mather's alpha-function arises from homogenized Floer homological Lagrangian spectral invariants and how it gives rise to the existence of an analogue of Mather measures (from Aubry-Mather theory) to general symplectic manifolds. Unlike what happens in the Tonelli case, I will show that the support of these measures can be extremely "wild" in the non-convex case. I will explain how this phenomenon is closely related to diffusion phenomena such as Arnol'd diffusion. The second approach builds on work due to Buhovsky-Entov-Polterovich and provides a C⁰-analogue of Mather measures for Hamiltonians on "flexible" symplectic manifolds. I will discuss applications to Hamiltonian systems on twisted cotangent bundles and R²ⁿ.
  
  
• Jaime Bustillo: A coisotropic non-squeezing theorem in symplectic geometry
  Abstract:
  I will explain how generating functions and Viterbo's capacities can be used to prove a coisotropic non-squeezing theorem for Hamiltonian diffeomorphisms of R²ⁿ generated by sub-quadratic Hamiltonians. We will then see the relation of this theorem with the middle dimensional symplectic rigidity problem. If I have time, I will briefly explain how this type of rigidity appears in the context of Hamiltonian PDEs or C⁰ symplectic geometry.
  
  
• Alexander Fauck: On manifolds with infinitely many fillable contact structures
  Abstract:
  A famous result by I. Ustilovsky states that on the odd dimensional spheres of dimension at least 5 there are infinitely many different fillable contact structures. In my talk, I will discuss how to extend this result to other differentiable manifolds, in particular manifolds which admit a periodic Reeb flow and connected sums of such manifolds. The main tool to distinguish the contact structures will be estimates on the Symplectic Homology of their fillings. In this context, we will look at contact structures admitting a sequence of contact forms such that the number of their periodic Reeb orbits in a fixed degree is bounded. This will provide us with the aforementioned estimates.
  
  
• Pazit Haim-Kislev: The EHZ capacity of convex polytopes
  Abstract:
  We introduce a simplification to the problem of finding a closed characteristic with minimal action for the special case of convex polytopes, which yields a combinatorial formula for the EHZ capacity. As an application, we show a certain subadditivity property of the capacity of a general convex body.
  
  
• Yang Huang: Convex hypersurface theory in higher-dimensional contact topology
  Abstract:
  Convex surface theory, introduced by Giroux in his thesis, plays a prominent role in 3-dimensional contact topology, including notably most of the classification results. In this talk I will outline a program which generalizes Giroux's theory to higher dimensions. No pre-knowledge on convex surface theory will be assumed. Joint work with Ko Honda.
  
  
• Cheuk Yu Mak: Tropically constructed Lagrangians in mirror quintic threefolds
  Abstract:
  In this talk, we will explain how to construct embedded closed Lagrangian submanifolds in mirror quintic threefolds using tropical curves and the toric degeneration technique. As an example, we will illustrate the construction for tropical curves that contribute to the Gromov-Witten invariant of the line class of the quintic threefold. The construction will in turn provide many homologous and non-Hamiltonian isotopic Lagrangian rational homology spheres, and a geometric interpretation of the multiplicity of a tropical curve as the weight of a Lagrangian. This is joint work with Helge Ruddat.
  
  
• Dusa McDuff: The stabilized symplectic embedding problem
• Stefan Nemirovski: Interval topology in contact geometry
  Abstract:
  An interval topology can be defined on spaces of Legendrians and on groups of contactomorphisms. The property of this topology to be Hausdorff reflects contact rigidity. The construction is motivated by and related to the so-called Alexandrov topology from Lorentz geometry. The talk is based on joint work with Vladimir Chernov.
  
  
• Gleb Smirnov: Lagrangian spheres in del Pezzo surfaces
  Abstract:
  It is known that two homologous Lagrangian spheres in the four-fold blowup of CP² are Hamiltonian isotopic. This was proven by J. Evans in his PhD thesis; he also noticed that the statement fails to be true for higher blow-ups. In this talk, we will classify Lagrangian spheres up to Hamiltonian isotopy for the five-fold blowup. This is a joint result with Sewa Shevchishin.
  
  
• Ivan Smith: Spherical objects on surfaces
  Abstract:
  I will discuss an ongoing attempt to understand the group of autoequivalences of the Fukaya category of a closed higher genus surface. This talk reports on joint work with Denis Auroux.
  
  

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