Cluster Algebras, Augmentations, and Legendrian Knots

Add to your list(s) Download to your calendar using vCal

• Linhui Shen (Michigan State University)
• Tuesday 09 November 2021, 14:30-15:00
• Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact nobody.

CARW03 - Interdisciplinary applications of cluster algebras

The theory of cluster algebras and the study of Legendrian knots, coming from the worlds of algebra and geometry respectively, are currently engaged in robust and fruitful dialogue. In this talk, we investigate positive-braid Legendrian links via a Floer-theoretic approach and prove that the coordinate ring of their augmentation varieties are cluster algebras. Using the exact Lagrangian cobordisms of Legendrian links developed by Ekholm-Honda-Kalman, we prove that the admissible Lagrangian fillings of positive-braid Legendrian links correspond to cluster seeds of their augmentation varieties. We solve the infinite-filling problem for positive-braid Legendrian links; i.e., whenever a positive-braid Legendrian link is not of type ADE , it admits infinitely many exact Lagrangian fillings. This talk is based on joint work with Honghao Gao and Daping Weng.

This talk is part of the Isaac Newton Institute Seminar Series series.

This talk is included in these lists:

• All CMS events
• Featured lists
• INI info aggregator
• Isaac Newton Institute Seminar Series
• School of Physical Sciences
• Seminar Room 1, Newton Institute
• bld31

Note that ex-directory lists are not shown.