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PhD Exit Seminar: Legendrian loops and cluster modular groups
Special Events| Speaker: | James Hughes, UC Davis |
| Location: | 2112 MSB |
| Start time: | Mon, May 22 2023, 12:10PM |
An exact Lagrangian filling of a Legendrian link L is a surface in the symplectic four-ball with boundary equal to L that respects the symplectic structure in some way. A Legendrian loop is an isotopy of a Legendrian link that fixes the link pointwise. Legendrian loops induce group actions on the space of exact Lagrangian fillings and have recently become crucial tools in the construction and classification of exact Lagrangian fillings.
In this talk I will describe some of these Legendrian loop actions and their properties. In particular, I will leverage the theory of cluster algebras to highlight analogies between Legendrian loop actions and mapping class groups, including a Nielsen-Thurston-like classification of Legendrian loops. Time permitting, I will also mention some applications of the study of Legendrian loops to exact Lagrangian fillings of Legendrian surfaces, developed in joint work with Agniva Roy.
Zoom Link: https://ucdavis.zoom.us/j/96986015365?pwd=WXg2TzJpTjZHMFNCelBJVnJiMTZNQT09
Meeting ID: 969 8601 5365, Passcode: 30952