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In search of Lagrangians with non-trivial Floer cohomology by Sushmita Venugopalan

190 views · Published 21 June 2018 · 1:03:10 · Indexed 20 September 2026

Channel: International Centre for Theoretical Sciences · 2018 · Science & Technology

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DISCUSSION MEETING
ANALYTIC AND ALGEBRAIC GEOMETRY

DATE:19 March 2018 to 24 March 2018
VENUE:Madhava Lecture Hall, ICTS, Bangalore.

Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions between mathematics and theoretical physics, especially string theory, channels through complex analytic geometry. Some of the high points of research in this topic are: Yau’s proof of Calabi’s conjecture, Donaldson- Uhlenbeck-Yau’s theorem that polystable vector bundles are precisely the solutions of the Hermitian-Einstein equation, Demailly’s work of Kobayashi hyperbolicity.


CONTACT US:[email protected]
PROGRAM LINK:https://www.icts.res.in/discussion-meeting/aag2018

Table of Contents (powered by https://videoken.com)
0:00:00 ICTS
0:00:05 In search of Lagrangian's with non-trivial Floer cohomology
0:00:10 In search of Lagrangian's with non-trivial cohomology
0:02:34 Towards Floer homology of a Lagrangian submanifold
0:03:57 -algebra
0:05:57 Homomorphic disks
0:09:59 Quick definition : Morse cohomology of a manifold M
0:15:49 Treed homomorphic disks
0:19:18 Aco -algebra of a Lagrangian
0:27:08 Some remarks
0:28:18 Floer cohomology of the Lagrangian
0:31:36 A geometric consequence of Floer non-triviality
0:34:40 Toric symplectic manifolds
0:38:22 Examples of symplectic toric manifolds
0:43:52 Floer non-triviality for toric Lagrangian's
0:48:09 Example: Point blow-up of projective space
0:50:36 Symplectic cuts
0:54:45 Idea of Charest-Woodward proof
0:56:59 Another example: line blow up
0:59:39 Conjectures, results

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