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Have you ever wondered why we describe circuits with matrices? I mean, circuits are about tensor products, while matrices are about direct sums. This new paper with @llemonnier and @manchegobaby.bsky.social gives a practically useful explanation: arxiv.org/abs/2510.05032.
The key is that circuits contain controlled gates. It's not quite data flow, nor control flow, in the usual computer science se
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Coverages, or Grothendieck topologies, describe when a collection of regions covers another region in a space. But what if your space is a spacetime? The topological space may have a causal order saying which (spacetime) points 'come before' which other points, for example.
Well, you don't need points to describe that, and can do it purely with open sets. This new paper with Nesta van der Schaaf d
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🔥 Top post: I really like this paper, with @JacquesC2, @rkaarsgaard , and Am · 87 likes + reposts
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Coverages, or Grothendieck topologies, describe when a collection of regions covers another region in a space. But what if your space is a spacetime? The topological space may have a causal order saying which (spacetime) points 'come befor…
So much material for titles here, too! "If you liked it you shoulda put a rig on it", "The rig is up", "Taking back control". What's your favourite?
Have you ever wondered why we describe circuits with matrices? I mean, circuits are about tensor products, while matrices are about direct sums. This new paper with @llemonnier and @manchegobaby.bsky.social gives a practically useful expla…
🚨 New preprint alert 🚨
Always wanted to know the connection between analytic limits and categorical limits? Tired of having to establish directed colimits of contractions when directed colimits of isometries suffice? You're in luck!
This …
The saga continues! Axioms for the category of finite-dimensional Hilbert spaces and linear contractions, with Matt Di Meglio, now on https://arxiv.org/abs/2401.06584.
After axiomatising Hilbert spaces and bounded linear maps, and Hilbert…
New paper alert! "Categories of sets with infinite addition", with Pablo Andres-Martinez, https://arxiv.org/pdf/2308.15183.
In a commutative monoid you can add finitely many elements. But why stop at finite? This paper is about sets where…
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