ItaCa Fest - Bonchi and Blechschmidt - 28 June

ItaCa Fest - Bonchi and Blechschmidt - 28 June

[Ivan Di Liberti]

Dear all,

The next date of the ItaCa Fest will be June 28, 2022 at 3 pm (Italian time):

- F. Bonchi,
- I. Blechschmidt.

The zoom link is the following: https://stockholmuniversity.zoom.us/j/68792232558
While the Fest website is this one: https://progetto-itaca.github.io/pages/fest22.html

Join us (and bring a friend)!

Cheers,
Beppe, Ivan, Edoardo, Fosco, Paolo.

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Bonchi.
Title: Deconstructing Tarski’s calculus of relations with Tape diagrams
Abstract: The calculus of (binary) relations has been introduced by Tarski as a variable-free alternative to first order logic. In this talk we introduce tape diagrams, a graphical language for expressing arrows of arbitrary finite biproduct rig categories, and we show how the calculus of relation can be encoded within tape diagrams.

Blechschmidt.
Title: Reifying dynamical algebra, Traveling the mathematical multiverse to apply tools for the countable also to the uncountable.
Abstract: Commutative algebra abounds with proofs which are quite elegant and at the same time quite abstract. Even for concrete statements, proofs often appeal to transfinite methods like the axiom of choice or the law of excluded middle. Following Hilbert’s call, we should work to elucidate how these abstract proofs can be recast in more concrete, computational terms, regarding abstract proofs as intriguing guiding templates for formulating concrete proofs and regarding objects concocted by Zorn’s lemma such as maximal ideals as convenient fictions. One such technique for making computational sense of abstract proofs is dynamical algebra, going back to the work of Dominique Duval and her coauthors in the 1980’s. The talk will first present the basic story of dynamical algebra with an illustrative example. Then we will report on joint work with Peter Schuster how to reify dynamical algebra using formal metatheorems of categorical logic, supplying a firm foundation to dynamical algebra, complementing previous approaches. A particular feature of our approach is that we apply a construction devised by Berardi and Valentini for the special case of countable rings, which indeed fundamentally requires the countability assumption, by a logical sleight of hand by Joyal and Tierney to arbitrary rings. This trick is applicable quite generally which is why we believe that it is of interest to a larger group of people. It is unlocked by categorical logic running on a certain fractal without points, the pointfree space of enumerations of a given set.

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