Preliminary program of the summer school
This is the program for the summer school. Here is the wiki page.
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Day 1: Legendrian contact homology (schedule)
General background on Legendrian submanifolds, holomorphic curves, Chekanov–Eliashberg differential graded algebra.
References:- Etnyre, Legendrian and transversal knots
- Chekanov, Differential algebra of Legendrian links
- Ng, Computable Legendrian invariants
- Ekholm, Etnyre, and Sullivan, Legendrian contact homology in P x R
- Ekholm, Morse flow trees and Legendrian contact homology in 1-jet spaces
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Day 2: Knot contact homology (schedule)
Cotangent bundles and the conormal construction, combinatorial and geometric formulations of knot contact homology, basic properties.
References:- Ng, A topological introduction to knot contact homology
- Ekholm and Etnyre, Invariants of knots, embeddings and immersions via contact geometry
- Ekholm, Etnyre, Ng, and Sullivan, Knot contact homology
- Ekholm, Etnyre, Ng, and Sullivan, Filtrations on the knot contact homology of transverse knots
- Ng, Framed knot contact homology
- Ng, Combinatorial knot contact homology and transverse knots
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Day 3: Augmentations and topological string theory (schedule)
Augmentation variety of a link, Chern–Simons theory, resolved conifold, fillings of the conormal Legendrian of a knot, Gromov–Witten potential.
References:- Mariño, Chern–Simons theory and topological strings
- Ooguri and Vafa, Knot invariants and topological strings
- Ekholm, Notes on topological strings and knot contact homology
- Aganagic, Ekholm, Ng, and Vafa, Topological strings, D-model, and knot contact homology
- Aganagic and Vafa, Large N duality, mirror symmetry, and a Q-deformed A-polynomial for knots
- Diaconescu, Shende, and Vafa, Large N duality, Lagrangian cycles, and algebraic knots
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Day 4: Sheaves and augmentations (schedule)
Constructible sheaves and singular support, rulings and generating families for Legendrian knots, augmentations and sheaves, KCH representations.
References:- Shende, Treumann, and Zaslow, Legendrian knots and constructible sheaves
- Fuchs and Rutherford, Generating families and Legendrian contact homology in the standard contact space
- Bourgeois and Chantraine, Bilinearised Legendrian contact homology and the augmentation category
- Ng, Rutherford, Shende, Sivek, and Zaslow, Augmentations are sheaves
- Cornwell, KCH representations, augmentations, and A-polynomials
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Day 5: String topology and flavors of Floer homology (schedule)
Symplectic homology, surgery formulae for critical handle addition, wrapped and partially wrapped Floer homology, string topology and the knot group.
References:- Bourgeois, Ekholm, and Eliashberg, Effect of Legendrian surgery
- Cieliebak, Ekholm, Latschev, and Ng, Knot contact homology, string topology, and the cord algebra
- Ekholm, Ng, and Shende, A complete knot invariant from contact homology
- Ekholm and Lekili, Duality between Lagrangian and Legendrian invariants
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