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1. • CommentRowNumber1.
   • CommentAuthorNoam_Zeilberger
   • CommentTimeDec 22nd 2016
   • PermaLink
   Author: Noam_Zeilberger
   Format: MarkdownItexAs a postscript to some discussion on virtual knot theory we had here [a little under a year ago](https://nforum.ncatlab.org/discussion/6901/virtual-knot-theory/#Item_1), I met [Victoria Lebed](http://www.maths.tcd.ie/~lebed/) yesterday and it turns out that she studied categorification questions (among other things) in her thesis! I've only skimmed it so far, but it seems very nice, and her approach to virtual braids is very much in the spirit of John Baez's n-Café comment. In particular, the thesis shows that the virtual braid group $VB_n$ is isomorphic to the group of endomorphisms $End_{\mathcal{C}_{2br}}(V^{\otimes n})$, where $\mathcal{C}_{2br}$ is the free symmetric monoidal category generated by a single [[braided object]] $V$. (The thesis also talks a lot about positive braids, which are interpreted in terms of "pre-braided" objects, i.e., an object $V$ equipped with a not necessarily invertible morphism $\sigma : V \otimes V \to V \otimes V$ satisfying the Yang-Baxter equation. This definition even allows for the possibility of "idempotent" braidings, which she mentioned in her talk yesterday.)

   As a postscript to some discussion on virtual knot theory we had here a little under a year ago, I met Victoria Lebed yesterday and it turns out that she studied categorification questions (among other things) in her thesis! I’ve only skimmed it so far, but it seems very nice, and her approach to virtual braids is very much in the spirit of John Baez’s n-Café comment. In particular, the thesis shows that the virtual braid group $VB_n$ is isomorphic to the group of endomorphisms $End_{\mathcal{C}_{2br}}(V^{\otimes n})$, where $\mathcal{C}_{2br}$ is the free symmetric monoidal category generated by a single braided object $V$. (The thesis also talks a lot about positive braids, which are interpreted in terms of “pre-braided” objects, i.e., an object $V$ equipped with a not necessarily invertible morphism $\sigma : V \otimes V \to V \otimes V$ satisfying the Yang-Baxter equation. This definition even allows for the possibility of “idempotent” braidings, which she mentioned in her talk yesterday.)

2. • CommentRowNumber2.
   • CommentAuthorNoam_Zeilberger
   • CommentTimeDec 22nd 2016
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   Author: Noam_Zeilberger
   Format: MarkdownItex(So on the "Latest changes" front, I've tried to incorporate this into the article on [[virtual knot theory]], and created [[braided object]].)

   (So on the “Latest changes” front, I’ve tried to incorporate this into the article on virtual knot theory, and created braided object.)

3. • CommentRowNumber3.
   • CommentAuthorTodd_Trimble
   • CommentTimeDec 22nd 2016
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   Author: Todd_Trimble
   Format: MarkdownItexHasn't she also studied the connection between braids and Laver tables in set theory? I seem to recall her name in connection with that.

   Hasn’t she also studied the connection between braids and Laver tables in set theory? I seem to recall her name in connection with that.

4. • CommentRowNumber4.
   • CommentAuthorNoam_Zeilberger
   • CommentTimeDec 22nd 2016
   • (edited Dec 22nd 2016)
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   Author: Noam_Zeilberger
   Format: MarkdownItexIt's possible (EDIT: rather, it's [true](http://www.maths.tcd.ie/~lebed/Lebed_ATS14_beamer.pdf))...her talk yesterday was on a connection between (idempotent!) braids and Young tableaux.

   It’s possible (EDIT: rather, it’s true)…her talk yesterday was on a connection between (idempotent!) braids and Young tableaux.

5. • CommentRowNumber5.
   • CommentAuthorTim_Porter
   • CommentTimeDec 22nd 2016
   • (edited Dec 22nd 2016)
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexShe gave a lovely talk in Leeds earlier this year (5-8 July 2016). The slides are [here](http://www1.maths.leeds.ac.uk/~matzk/Modelling%20TPM%20Resources_files/Crossed.pdf). I have added the link. Her webpage at Trinity mentions Laver tables.

   She gave a lovely talk in Leeds earlier this year (5-8 July 2016). The slides are here. I have added the link.

   Her webpage at Trinity mentions Laver tables.