Tubular neighborhoods and holomorphic curves.

Tubular neighborhoods and holomorphic curves.

Tubular neighborhoods and holomorphic curves.

Monday, January 12, 2026
  • Lecturer: Sara Tukachinsky (TAU)
  • Organizer: Ilya Gekhtman and Yatir Halevi
  • Location: Room 814, Amado Mathematics Building
Abstract:
Abstract: In studying the geometry of smooth manifolds, one fundamental problem is that of telling apart different submanifolds. By "telling apart" we could mean various things, for example, we could ask whether or not two given submanifolds are isotopic to one another.  A typical way of showing two submanifolds are non-isotopic is to find an invariant that is preserved under isotopy but takes different values on the two submanifolds. In symplectic geometry, a submanifold of particular importance is a Lagrangian submanifold, and telling those apart is important accordingly. One isotopy invariant associated to a Lagrangian submanifold is the count of (pseudo-)holomorphic disks with boundary condition in the Lagrangian. Surprisingly enough, the analysis of such holomorphic disks can be carried out in a small tubular neighborhood of the Lagrangian. In this talk, I will illustrate the above problem in the most classical example of two Lagrangian tori in the complex plane \C^2. I will then introduce an ongoing project, joint with Yael Karshon and our student Yoav Zimhony, where we aim at applying similar ideas to new settings. As a first step, we give a tubular neighborhood theorem for certain singular Lagrangians. No prior knowledge in symplectic geometry will be assumed. "Light refreshments will be served at 15:00 at the faculty lounge on the 8th floor."
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