CRM-Montreal Symplectic Seminar - Room 4336 Building André Aisenstadt, UdeM : Sheet1

1 | Speaker | Date | Hour | Title | Abstract |
---|---|---|---|---|---|

2 | Leonid Polterovich (Tel Aviv and SCGP Stony Brook) | 9/24/2012 | 16:00 - 17:00 | Symplectic geometry of quantum noise | We discuss a quantum counterpart, in the sense of the Berezin-Toeplitz quantization, of certain constraints on Poisson brackets coming from "hard" symplectic geometry. It turns out that they can be interpreted in terms of the quantum noise of observables in operational quantum mechanics. |

3 | Egor Shelukhin (CRM-Montreal) | 10/15/2012 | 15:00 - 16:00 | Almost complex structures and quasimorphisms | We recall a construction of a quasimorphism on the universal cover of the Hamiltonian group of any closed symplectic manifold, and show some calculations in the presence of a trivialization. |

4 | Strom Borman (Chicago) | 11/12/2012 | 14:30 - 15:30 | The width of a Lagrangian | The width of a Lagrangian is the largest capacity of ball that can be symplectically embedded into the ambient manifold such that the ball intersects the Lagrangian exactly along the real part of the ball. In this talk I will present a wrapped Floer cohomology construction that can upper bound a Lagrangian's width in terms of its displacement energy. This is joint work in progress with Mark McLean. |

5 | Johannes Walcher (McGill) | 11/26/2012 | 14:30 - 15:30 | On the (ir)rational(e) of counting holomorphic disks | I will review the basic ideas underlying the counting of holomorphic disks ending on Lagrangians in Calabi-Yau threefolds via mirror symmetry. The most recent calculations appear to predict counts that are irrational (but algebraic) numbers. I will argue for the what and why this makes sense. |

6 | Milena Pabiniak (Toronto) | 12/3/2012 | 14:30 - 15:30 | Lower bounds on Gromov width of coadjoint orbits through the Gelfand-Tsetlin pattern | Gromov width of a symplectic manifold M is a supremum of capacities of balls that can be symplectically embedded into M. Let G be a compact connected Lie group G, T its maximal torus, and $\lambda$ be a point in the chosen positive Weyl chamber. The coadjoint orbit through $\lambda$ is canonically a symplectic manifold, therefore we can ask the question of its Gromov width. In many known cases the width is exactly the minimum over the set of positive results of pairing $\lambda$ with coroots of G (for example if G=U(n) and the orbit is a complex Grassmannian). We use the torus action coming from the Gelfand-Tsetlin system to construct symplectic embeddings of balls and prove that the above formula gives the lower bound for Gromov width of U(n) and SO(n) coadjoint orbits. In the talk I will describe the Gelfand-Tsetlin system and concentrate mostly on the case of regular U(n) orbits. |

7 | Lara Suarez Lopez (UdeM) | 12/10/2012 | 14:30 - 15:30 | Lagrangian cobordism | It was shown by Biran and Cornea that if two uniformly monotone Lagrangian submanifolds are Lagrangian cobordant via a monotone Lagrangian cobordism, then their quantum homologies coincide. We will use this fact to show that a simply connected exact Lagrangian cobordism between exact and simply connected Lagrangians is an h-cobordism. |

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9 | Max Lyapinsky | 3/18/2013 | 14:00 - 15:00 | Semi-Infinite Cycles in Floer Theory | I will describe a new construction of Floer theories based on a notion of "semi-infinite" geometric cycle. As opposed to the traditional Morse-theoretic approach, no transversality/nondegeneracy assumptions are necessary for the definition. I will illustrate the theory with examples from gauge theory and symplectic geometry. |

10 | Emmy Murphy (MIT) | 3/25/2013 | 14:30 - 15:30 | Lagrangian caps in high dimensional symplectic manifolds | I will present a recent result (joint with Yakov Eliashberg) demonstrating the existence of exact Lagrangian cobordisms with a loose Legendrian in the negative end, in all dimensions greater than 4. In particular we show that there exists a Lagrangian disk in \C^n \ B^{2n} which has Legendrian boundary in S^{2n-1}, whenever n>2. It is known there are no such disks in \C^2. The proof showcases a new “Lagrangian Whitney trick”. As an application, we prove a universal embedding theorem for flexible Weinstein manifolds, showing in particular that any Weinstein manifold has interesting geometry only in a topological collar of the boundary. We also construct exact Lagrangian immersions with fewer intersections than the “philosophy of the Arnold conjecture” would predict (this application is joint with Tobias Ekholm, Eliashberg, and Ivan Smith). |

11 | Bulent Tosun (UQAM) | 4/8/2013 | 14:30 - 15:30 | Cabling and Legendrian simplicity | This talk will be about Legendrian and transverse knots in cabled knot types in the standard contact three sphere and their classifications up to contact isotopy. The classification results I will explain exhibit many new phenomena about structural understanding of Legendrian and transverse knot theory. The key ingredient of the proofs will be understanding of certain quantities associated to contact solid tori representing a knot type in the standard contact three sphere. Part of the results are joint work with John Etnyre and Douglas LaFountain. |