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UID:f31a081c39138d3241bb8d25df516736
CATEGORIES:Symplectic Geometry Seminar
CREATED:20240130T140815
SUMMARY:Augmentation Varieties and Disk Potential
LOCATION:Hill 705
DESCRIPTION:<p dir="ltr" style="line-height: 1.6667; margin-left: 15pt; margin-top: 9pt
 ; margin-bottom: 0pt;"><span style="font-size: 11pt; font-family: Lato; col
 or: #212121; background-color: transparent; font-weight: 400; font-style: n
 ormal; font-variant: normal; text-decoration: none; vertical-align: baselin
 e; white-space: pre-wrap;">Abstract: Dimitroglou-Rizell-Golovko constructs 
 a family of Legendrians in prequantization bundles by taking lifts of monot
 one Lagrangians. These lifted Legendrians have a Morse-Bott family of Reeb 
 chords. We construct a version of Legendrian Contact Homology(LCH) for Rize
 ll-Golovko's lifted Legendrians by counting treed disks. Our formalism of L
 CH allows us to obtain augmentations from certain non-exact fillings. We pr
 ove a conjecture of Rizell-Golovko relating the augmentation variety assoic
 iated to the LCH of a lifted Legendrian and the disk potential of the base 
 Lagrangian. As an application, we show that lifts of monotone Lagrangian to
 ri in projective spaces with different disk-potentials, e.g. as constructed
  by Vianna, produce non-isotopic Legendrian tori in contact spheres. The ab
 ove work is a joint project with Blakey, Sun and Woodward.</span></p>
CONTACT:Soham Chanda (Rutgers)
DTSTAMP:20260828T183952
DTSTART;TZID=America/New_York:20240201T133000
DTEND;TZID=America/New_York:20240201T143000
SEQUENCE:0
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