Geometry/Physics Seminar

Title: Infinitely many Lagrangian Tori in Milnor fibers constructed via Lagrangian Fillings of Legendrian links
Speaker: Orsola Capovilla-Searle
Speaker Info: Duke University
Brief Description: Virtual (Zoom) Talk
Special Note:

Meeting ID: 916 7431 9341

Meeting Password: First word of the name of the seminar (in small letters)

Abstract: One approach to studying symplectic manifolds with contact boundary is to consider Lagrangian submanifolds with Legendrian boundary; in particular, one can study exact Lagrangian fillings of Legendrian links. There are still many open questions on the spaces of exact Lagrangian fillings of Legendrian links in the standard contact 3-sphere, and one can use Floer theoretic invariants to study such fillings.

We show that family of oriented Legendrian links has infinitely many distinct exact orientable Lagrangian fillings up to Hamiltonian isotopy. We provide some of the first examples of a Legendrian link that admits infinitely many planar exact Lagrangian fillings. Weinstein domains are examples of symplectic manifolds with contact boundary that have a handle decomposition compatible with the symplectic structure of the manifold. Weinstein handlebody diagrams are given by projections of Legendrian submanifolds. We provide Weinstein handlebody diagrams of the $4$-dimensional Milnor fibers of $T_{p,q,r}$ singularities, which we then use to construct infinitely many Lagrangian tori and spheres in these spaces.

Date: Thursday, May 20, 2021
Time: 3:00pm
Where: Meeting ID: 916 7431 9341
Contact Person: Dogancan Karabas
Contact email: dogancan.karabas@northwestern.edu
Contact Phone:
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