Caen Workshop on v- and w-Knotted Objects

Valeriy Bardakov, Jean-Baptiste Meilhan, Paolo Bellingeri, Sakie Suzuki, Benjamin Audoux, Karene Chu, Nathan Habegger, Dror Bar-Natan, Emmanuel Wagner, Anne-Laure Thiel, Adrien Brochier, Bruno Cisneros.

See Also: The organizer's web site, blackboard shots, my notebook, the WKO website.

Wednesday June 6:

• Paolo Bellingeri on Groups of Virtual and Welded Links.
• My June 6 Clip 1: General introduction and "the menu" (see the handout).
• My June 6 Clip 2: The general notion of "projectivization".
• My June 6 Clip 3: All about wB_n, from the definition to the interpretation of its homomorphic expansion in terms of flows on a Lie algebra/group.

Thursday June 7:

• Eddy Godelle on Garside Structures for Virtual Braids (no video).
• Anne-Laure Thiel on Categorification of Virtual Braids.
• My June 7 Clip 1: Circuit algebras, virtual braids, braid-like and cyclic Reidemeister moves, the Roman XII relation.
• My June 7 Clip 2: A^w, bracket-rise, wheels and trees and free Lie algebras.

Friday June 8:

• Valeriy Bardakov on Residual Properties for Virtual and Welded Braids.
• Bruno Cisneros on Stable Equivalence of Knots on Surfaces.

My session was about the talk "Meta-Groups, Meta-Bicrossed-Products, and the Alexander Polynomial" I gave in Regina a week before. We watched the video from that talk and interupted it a number of times for comments, and at the end had a lengthy discussion with many more comments. See the talk page and handout and especially the talk video.

• My June 8 Clip 1: The plan for today.
• My June 8 Clip 2: Comment on minute 5:56 - the "popped-up membranes" view of w-knots.
• My June 8 Clip 3: Comment on minute 44:48 - changes needed for the multi-variable case.
• My June 8 Clip 4: Comment on minute 46:27 - reading out the ugly formulas.
• My June 8 Clip 5: After-video planning.
• My June 8 Clip 6: The main discussion - going through the slides again, examples, my "to do" list (on meta matters) in detail.

Saturday June 9: (at Juno beach)

Sunday June 10: (at Château de Caen)

June 11 Handout.

Monday June 11:

• Sakie Suzuki on the Universal sl2 Invariant of Brunnian Bottom Tangles.
• Adrien Brochier on Cyclotomic Associators and Finite Type Invariants for Tangles in the Solid Torus.

In my session we followed the handout "Some Details for the Caen Workshop, 1". See Details-1.html, Details.pdf, Details-1.png and the source files at Details.zip. (The other side was propaganda).

• My June 11 Clip 1: Wheels, trees, div, and their differential geometric interpretation.
• My June 11 Clip 2: Clarifying the AT-w-KV map, the AT div and its relationship with the w div.
• My June 11 Clip 3: Algebraic knot theory, the whole u→w algebraic structure, and the double-tree construction.

Tuesday June 12:

• Karene Chu on Flat Virtual Pure Tangles.
• Jean-Baptiste Meilhan on Milnor Invariants and the HOMFLYPT Polynomial.
• My June 12 Clip 1: Clarifying the local structure of w-knotted objects, the twist relation, excellence conditions on associators, which is what in the relationship between u→w, KV, AT, and AET.
• My June 12 Clip 2: The w-side equations (R4, unitarity, disk-unzip), jacobians, proof of the equivalence with the AT version of the KV equations.

June 12 Colloquium.

Colloquium: My June 12 Colloquium on Cosmic Coincidences and Several Other Stories (the PDF and sources for the handout are at Tennessee-1103).

Wednesday June 13:

• Paolo Bellingeri showed and explained some wonderful movies by Ester Dalvit on braids, dances, wickets, and the Hilden group, and discussed some papers by Stephen Tawn.
• Emmanuel Wagner on the Jaeger Expansion of Kauffman Polynomial.
• My June 13 Clip 1: The local structure of vertices, three formulations of the u→w maps, the beta relations, "wheeling" in the w-world.
• My June 13 Clip 2: beta-calculus: the four basic operations, an evaluation example with the virtual trefoil, the origin of the terms in the swap formula.

Thursday June 14:

• My June 14 Clip 1: The topological side of beta-calculus, the Euler trick and applications, the scheme of the Euler computation of Alexander.
• Adrien Brochier on A Cohomological Construction of Quantization Functors of Lie Bialgebras (Following B. Enriquez).