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SUMMARY:Cluster Algebras\, Augmentations\, and Legendrian Knots - Linhui S
 hen (Michigan State University)
DTSTART:20211109T143000Z
DTEND:20211109T150000Z
UID:TALK164770@talks.cam.ac.uk
DESCRIPTION:The theory of cluster algebras and the study of Legendrian kno
 ts\, coming from the worlds of algebra and geometry respectively\, are cur
 rently engaged in robust and fruitful dialogue. In this talk\, we investig
 ate positive-braid Legendrian links via a Floer-theoretic approach and pro
 ve that the coordinate ring of their augmentation varieties are cluster al
 gebras. Using the exact Lagrangian cobordisms of Legendrian links develope
 d by Ekholm-Honda-Kalman\, we prove that the admissible Lagrangian filling
 s 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.
LOCATION:Seminar Room 1\, Newton Institute
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