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Are there any nice discussions of applications of small cancellation theory, or other cases of the word problem, in applied mathematics or algorithms for seemingly non-group theoretic problems?

I suppose two candidates are Anshel–Anshel–Goldfeld key exchange and braid group based cryptography.

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  • $\begingroup$ Jeff, I got your email and replied. If you do not get my reply, please let me know, here I guess. I made this a "favorite" question, I will automatically be able to find this. $\endgroup$
    – Will Jagy
    Sep 26, 2011 at 4:44
  • $\begingroup$ Braid group based cryptography was popular at the very beginning of the 21st century when the Anshel-Anshel-Goldfeld key exchange was originally invented, but today people view braid group cryptography as insecure. $\endgroup$ Apr 25, 2017 at 16:11

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The group-based cryptography is a very active area now. There are books (eg Group-based Cryptography) and a special journal, Groups Complexity Cryptology.

As another application, one can reformulate the problem P=NP as "Is it true that every finitely presented group with polynomial Dehn function has word problem solvable deterministically in polynomial time?" (see the paper Isoperimetric and isodiametric functions of groups arXiv:math/9811105).

Small cancelation itself is not used much in any of these areas, but many ideas are inspired by the classical small cancelation theory.

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