[HoTT] HoTT combinatorics

[HoTT] HoTT combinatorics

[Andrej Bauer]

In a couple of days I am gonig to give a talk about HoTT in front of
250 combinatorialists at http://fpsac2019.fmf.uni-lj.si

I have some ideas about how to explain that HoTT is relevant to a
mathematician who studies "simple finite objects", but I'd be
interested to hear if anyone has anything else to say. I'll gladly
acknowledge good ideas.

My current plan is to discuss, after a suitable introduction:

1. The difference between Σ and ∃ is the difference between "explicit
construction" and "abstract proof of existence".

2. Discuss univalence and how we get "isomorphic structures are equal".

3. I will advertise Brent Yorgey's PhD thesis about combinatorial
spieces, and probably cite some gems from it
(https://homotopytypetheory.org/2016/07/20/combinatorial-species-and-finite-sets-in-hott/)

I don't have a good feeling for what might pique a combinatorialist's
interest. Does anyone here?

With kind regards,

Andrej

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Re: [HoTT] HoTT combinatorics

[Gabriel Scherer]

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Not HoTT-specific, some of the recent type/proof-theory work of Noam
Zeilberger may pique the interest of combinatorists. For example,

  A sequent calculus for the Tamari order
  Noam Zeilberger, 2019
  https://arxiv.org/abs/1803.10080

uses a sequent calculus to describe the structure of an order relation on
trees that combinatorist have studied, and re-derive counting results on
the intervals of that order.

(Reasoning on the structure of an order relation is not too far from the
"higher" concerns of HoTT and higher category-theory.
And the idea of using adequate proof structures to prove a coherence result
has been used in many other more categorical settings.)

On Mon, Jul 1, 2019 at 1:36 PM Andrej Bauer <andrej.bauer@andrej.com> wrote:

> In a couple of days I am gonig to give a talk about HoTT in front of
> 250 combinatorialists at http://fpsac2019.fmf.uni-lj.si
>
> I have some ideas about how to explain that HoTT is relevant to a
> mathematician who studies "simple finite objects", but I'd be
> interested to hear if anyone has anything else to say. I'll gladly
> acknowledge good ideas.
>
> My current plan is to discuss, after a suitable introduction:
>
> 1. The difference between Σ and ∃ is the difference between "explicit
> construction" and "abstract proof of existence".
>
> 2. Discuss univalence and how we get "isomorphic structures are equal".
>
> 3. I will advertise Brent Yorgey's PhD thesis about combinatorial
> spieces, and probably cite some gems from it
> (
> https://homotopytypetheory.org/2016/07/20/combinatorial-species-and-finite-sets-in-hott/
> )
>
> I don't have a good feeling for what might pique a combinatorialist's
> interest. Does anyone here?
>
> With kind regards,
>
> Andrej
>
> --
> You received this message because you are subscribed to the Google Groups
> "Homotopy Type Theory" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to HomotopyTypeTheory+unsubscribe@googlegroups.com.
> To view this discussion on the web visit
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> .
> For more options, visit https://groups.google.com/d/optout.
>

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