The Informal Symplectic Geometry Seminar meets in Math 507, usually from 5:30-7:00, sometimes on Mondays. Its main purpose is to provide detailed introductions to recent developments in symplectic geometry and related fields through multi-part talks.

The Informal Symplectic Geometry Seminar should not be confused with Columbia's more traditional Symplectic Geometry and Gauge Theory seminar, which meets on Fridays from 1:00-2:00, or the Eilenberg Lectures on "Symplectic topology of affine complex manifolds.".

Date | Speaker | Title |
---|---|---|

Sept. 10 (Monday) | András Stipsicz (Rényi Institute / Columbia) | Contact structures on Seifert fibered three-manifolds, part 1. |

Sept. 21 (Friday), 10:00-11:30 | András Stipsicz (Rényi Institute / Columbia) | Contact structures on Seifert fibered three-manifolds, part 2. |

Sept. 24 (Monday) | András Stipsicz (Rényi Institute / Columbia) | Contact structures on Seifert fibered three-manifolds, part 3. |

Oct. 1 (Monday) | Tim Perutz (Columbia) | Lagrangian correspondences for fibered four-manifolds, part 1. |

Oct. 8 (Monday) | Lenhard Ng (Duke) | |

Oct. 15 (Monday) | Tim Perutz (Columbia) | Lagrangian correspondences for fibered four-manifolds, part 2. |

Oct. 22 (Monday) | R. Inanc Baykur (Columbia) | Topology of broken Lefschetz fibrations. |

Oct. 29 (Monday) | Tim Perutz (Columbia) | Lagrangian correspondences for fibered four-manifolds, part 3. |

Nov. 5 | No seminar this week. | |

Nov. 12 (Monday) | Tim Perutz (Columbia) | Lagrangian correspondences for fibered four-manifolds, part 4. |

Nov. 19 | No seminar this week. | |

Nov. 26 | No seminar this week. | |

Dec. 3 | No seminar this week. | |

Dec. 10 | No seminar this week. |

# Abstracts.

#### September 10, 2007.

Andras Stipsicz, "Contact structures on Seifert fibered three-manifolds, part 1."

#### September 21, 2007, 10:00 - 11:30 a.m.

Andras Stipsicz, "Contact structures on Seifert fibered three-manifolds, part 2."

#### September 24, 2007, 5:30-7:00 p.m.

Andras Stipsicz, "Contact structures on Seifert fibered three-manifolds, part 3."

#### October 1, 2007, 5:30-7:00 p.m.

Tim Perutz, "Lagrangian correspondences for fibered four-manifolds, part 1."

Abstract: The Heegaard Floer homology theory of Ozsvath and Szabo analyzes 3- and 4-manifolds in terms of their simplest pieces, namely, handles. I will describe a related but still incomplete theory, which aims to analyze 4-manifolds via the simplest constituents of certain singular fibrations over surfaces. The set-up involves, in three dimensions, circle-valued Morse functions without extrema, and in four dimensions, the "singular Lefschetz fibrations" introduced by Auroux, Donaldson and Katzarkov.

Like Heegaard Floer homology, the theory invokes symmetric products of surfaces, and it appears to recover Seiberg-Witten gauge theory symplectically. The crucial ingredient is a construction of Lagrangian correspondences between symmetric products. The development of this theory runs parallel to the study of a special class of submanifolds of symplectic manifolds, the spherically-fibred coisotropic submanifolds. According to work in progress, there are two interesting exact triangles in symplectic Floer homology associated with these submanifolds - counterparts of surgery and connected sum triangles in geometric topology.

In the first lecture, after a brief overview, I'll discuss "symplectic Morse-Bott fibrations", their vanishing cycles, and associated moduli spaces of pseudo-holomorphic curves.

#### October 8, 2007, 5:30-7:00 p.m.

Lenhard Ng, "Arc index, braid index, and Legendrian knots."

Abstract: What do arc index and braid index for knots have to do with contact geometry? I'll discuss a partly conjectural picture relating these invariants to Legendrian knots, and explain how they can often be computed using inequalities from contact geometry. I'll also describe how a bit of knowledge about Legendrian knots can sometimes help to calculate knot Floer homology, by providing minimal grid diagrams for some knots.

#### October 15, 2007, 5:30-7:00 p.m.

Tim Perutz, "Lagrangian correspondences for fibered four-manifolds, part 2."

Abstract: see part 1.

#### October 22, 2007, 5:30-7:00 p.m.

R. Inanc Baykur, "Topology of broken Lefschetz fibrations."

#### October 29, 2007, 5:30-7:00 p.m.

Tim Perutz, "Lagrangian correspondences for fibered four-manifolds, part 3."

Abstract: see part 1.

#### November 12, 2007, 5:30-7:00 p.m.

Tim Perutz, "Lagrangian correspondences for fibered four-manifolds, part 4."

Abstract: see part 1.

# Other relevant information.

## Our e-mail list.

Announcements for this seminar, as well as for related seminars and events, are sent to the "Floer Homology" e-mail list maintained via Google Groups. You can subscribe directly via Google Groups or by contacting R. Lipshitz.