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wClips-120418

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Videography by Sam Selmani

Notes on wClips-120418:    [edit, refresh]

Aside on the Euler trick, the differential of \exp, and the BCH formula.


[edit]

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Resources. How to use this site, Dror's notebook, blackboard shots.

The wClips

http://katlas.math.toronto.edu/drorbn/dbnvp/dbnvp.png
Date Links
Jan 11, 2012 dbnvp 120111-1: Introduction.
dbnvp 120111-2: Section 2.1 - v-Braids.
Jan 18, 2012 dbnvp 120118-1: An introduction to this web site.
dbnvp 120118-2: Section 2.2 - w-Braids by generators and relations and as flying rings.
dbnvp 120118-3: Section 2.2 - w-Braids - other drawing conventions, "wens".
Jan 25, 2012 dbnvp 120125-1: Section 2.2.3 - basis conjugating automorphisms of F_n.
dbnvp 120125-2: A very quick introduction to finite type invariants in the "u" case.
Feb 1, 2012 dbnvp 120201: Section 2.3 - finite type invariants of v- and w-braids, arrow diagrams, 6T, TC and 4T relations, expansions / universal finite type invariants.
Feb 8, 2012 dbnvp 120208: Review of u,v, and w braids and of Section 2.3.
Feb 15, 2012 dbnvp 120215: Section 2.5 - mostly compatibilities of Z^w, also injectivity and uniqueness of Z^w.
Feb 22, 2012 dbnvp 120222: Section 2.5.5, \alpha:{\mathcal A}^u\to{\mathcal A}^v, and Section 3.1 (partially), the definition of v- and w-knots.
Feb 29, 2012 dbnvp 120229: Sections 3.1-3.4: v-Knots and w-Knots: Definitions, framings, finite type invariants, dimensions, and the expansion in the w case.
Mar 7, 2012 dbnvp 120307: Section 3.5: Jacobi diagrams and the bracket-rise theorem.
Mar 14, 2012 dbnvp 120314: Section 3.6 - the relation with Lie algebras.
Mar 21, 2012 dbnvp 120321: Section 4 - Algebraic Structures.
Mar 28, 2012 Out-of-sequence not-on-tape we watched the video of Talks: GWU-1203.
Apr 4, 2012 dbnvp 120404: Section 3.7 - The Alexander Theorem (statement).
Apr 18, 2012 dbnvp 120418: Aside on the Euler trick, the differential of \exp, and the BCH formula.
Apr 25, 2012 dbnvp 120425: Section 3.8, a disorganized lecture towards the proof of the Alexander theorem.
May 2, 2012 dbnvp 120502: Section 4: Algebraic structures (review), circuit algebras, v- and w-tangles.
May 10, 2012 dbnvp 120510: Sections 5.1 and 5.2: tangles, their projectivization and its relationship with Alekseev-Torossian spaces.
May 23, 2012 dbnvp 120523: Section 5.2: Proof of the relationship with A-T spaces.
May 30, 2012 dbnvp 120530: Interpreting {\mathcal A}^w(\uparrow_n) as a universal space of invariant tangential differential operators.
wClips Seminar Group Photo
Group photo on January 11, 2012: DBN, ZD, Stephen Morgan, Lucy Zhang, Iva Halacheva, David Li-Bland, Sam Selmani, Oleg Chterental, Peter Lee.
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0:00:00 [edit] Blackboard shots by Stephan Morgan. Today's handout:

http://katlas.math.toronto.edu/drorbn/AcademicPensieve/Classes/12-wClips/Handout_for_April_18_and_25_400.jpg

The full size handout is at Pensieve: Classes: 12-wClips.

0:00:46 [edit] A cheese grater.
0:06:32 [add] Statement of the Alexander Theorem.
0:11:55 [add] Detached wheels and hairy Y's.
0:15:46 [add] The Euler Trick.
0:21:44 [add] The Euler Trick (2).
0:28:37 [add] The Euler Trick (3).
0:39:18 [add] The BCH Formula.
0:48:38 [add] The Differential of the Exponential Function.
0:57:36 [add] The Differential of the Exponential Function (2).
1:04:06 [add] The Differential of the Exponential Function (3).
1:11:11 [add] The BCH Formula (2).
1:20:10 [add] The BCH Formula (3).