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Description:
Description:
This seminar will be held in a hybrid format. We will meet on Tuesdays at 4-5pm Eastern in Maloney 560, as well as on zoom at the following Meeting ID: 919 3588 3118. Password is the name of the insect with its own special configuration, as shown in the picture below:
Organizers: Imogen Montague (montagui(at)bc.edu) and Mira Wattal (wattal(at)bc.edu)
Schedule:
Schedule:
Lecture 1-2 (1/23, 1/30): Sections 1-4 of [LS1] (Lecture 1 Notes)
Framed flow categories and their realizations as (cubical) CW-complexes
The cube flow category
Lecture 3-4 (2/6, 2/13): Section 5 of [LS1]
The Khovanov flow category
Ladybug matching and the moduli spaces associated to decorated resolution configuration diagrams
The definition of the Khovanov homotopy type
Lecture 5 (2/20): Field Trip!
Lecture 6 (2/27): Section 6 of [LS1]
Well-definedness and invariance of the homotopy type and explicit computations: Section 6 and 9
Lecture 7 (3/5): Break!
Lectures 8-9 (3/12, 3/19): [LS3]
Abstract Steenrod squares and Steenrod squares in Khovanov homology
An application to the Khovanov homotopy types of links with at most 11 crossings
Lecture 10 (3/26): [R]
Spectral sequences and the Lee deformation
The s-invariant
Lectures 11-12 (4/2, 4/9): [LS2]
Steenrod operations reprise and improvements of the s-invariant
Computations
Lectures 13 (4/16): Sections 1-4 of [LLS2]
Cube categories, Burnside categories, and the functors between them
Lectures 14-15 (4/23, 4/30): Sections 5-7 of [LLS2], [LLS1]
Properties of the functors between cube categories and Burnside categories and (suggestive) examples
The Khovanov functor
Remaining lectures: further applications (e.g., [LLS3]) or elucidations, and guest seminars
Resources:
Resources:
[LS1] A Khovanov stable homotopy type: https://arxiv.org/pdf/1112.3932.pdf
[LS2] A refinement of Rasmussen’s s-invariant: https://arxiv.org/pdf/1206.3532.pdf
[LS3] A Steenrod square on Khovanov homology: https://arxiv.org/pdf/1204.5776.pdf
[LLS1] Khovanov homotopy type, Burnside category, and products: https://arxiv.org/pdf/1505.00213.pdf
[LLS2] The cube and the Burnside category: https://arxiv.org/pdf/1505.00512.pdf
[LLS3] Khovanov spectra for tangles: (https://arxiv.org/pdf/1706.02346.pdf)
[R] Khovanov homology and the slice genus: https://arxiv.org/pdf/math/0402131.pdf
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