[Alta-Logic] Peripatetic Seminar for 07 February 2025

[Geoff Vooys]

Hi Everybody,

This week in the Peripatetic Seminar we will have one of Robin's MSc. students, Durgesh, speak about some categorical quantum mathematics. The talk details follow the body of this email. I hope to see you all there tomorrow!

Cheers,
Geoff

Title: Generalising the Coecke-Pavlovic-Vicary Correspondence

Time: Friday 07 February 2025, 14:00

Place: ICT 616

Abstract:

In their paper [1], Coecke-Palvovic-Vicary (CPV) gives a correspondence between orthogonal bases in finite-dimensional Hilbert Spaces (FdHilb) and Commutative-Dagger Frobenius algebras in FdHilb. In the first part of my talk, I will go over this correspondence and the associated categorical statements.

In the second part of my talk, I will give an outline of the programme about how this correspondence can be generalised to arbitrary dimensions. I will first introduce the ingredients involved- Finiteness spaces, Lefschetz Spaces and time-permitting linear monoids and then will give a few results connecting these mathematical objects.

Reference:
[1] Coecke, B., Pavlovic, D., & Vicary, J. (2012). A new description of orthogonal bases. Mathematical Structures in Computer Science, 23(3).

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