Conor Sheridan

Here is this weeks blog post: Geometry from Algebra III: From carriers to formal expressions conorsheridan111388.substack.com/p/geometry-f...

A bit of abstract nonsense: arxiv.org/pdf/2504.11099

Pretty cool paper: arxiv.org/pdf/2411.11568

Here is this weeks substack: Geometry from Algebra II: Free models and the semantic carrier conorsheridan111388.substack.com/p/geometry-f...

AI in math is like high-level programming: it changes the unit of thought. Proofs become components in larger structures, freeing attention for how theories fit together. The goal is understanding; AI adds abstraction. The concern is its use for manipulation, dominance, and oppression.

Nine and a half months after applying for a PhD, Glasgow has finally resolved the application. Rejected due to “the high level of competition.” Good to have closure on one of 2026’s longer-running open problems.

I would very much like to work on designing and implementing a type theory capable of verifying proofs and constructions in spectral algebraic geometry. What would be needed for such a thing? Intuitively something like a dependent differential linear homotopy type theory?

I’ve put up a paper version of some recent work on non-Cartesian internal categories and distributors. The main idea is a poly-virtual calculus that lets the relevant category and distributor operations be defined without assuming cotensors exist. tinyurl.com/y95ynfyn

This weeks essay became very long so I've split it into a 5 part series. Here is this weeks post on part I: Lawvere theories as spaces of operations , the next post will be available around this time next Friday! tinyurl.com/4kve5rfj

You all know that problems and proofs aren't a finite resource, right?

Is there a generalisation of the noncartesian internal categories of Aguilar and the generalized multicategories of Shulman&Crutwell? They don't seem to play very nicely together, or is this just my imagination?

People should have a legally protected right to use AI without surrendering the plaintext of their conversations to AI providers. Cryptographically verifiable confidential inference needs to become the required standard as the technology matures.

In order to improve my writing skills I've started a blog! I’m aiming to write one expository essay a week. The first is Spectra from a Logical Perspective, you can see it at either of the following links: Substack: tinyurl.com/z979axay PDF: tinyurl.com/3bnke68c

My old notes on fuzzy logic have evolved, first into a higher enriched form and via stabilization into a spectral information geometry! I have two more chapters to finish: Blackwell information and thermodynamics, then I'll release the notes as a milestone here on social media.

Besides theoretical computer science, I’ve had a long-term interest in the geometry of physics. I’ve now put the first public version of that project on GitHub. If category-theoretic geometry interests you: tinyurl.com/ds8jnhbs

What is the categorification of a Turing machine?

Species/symmetric sequences have a natural bosonic Fock calculus; Kapranov links supergeometry to stable homotopy. Has anyone combined these, e.g. by stabilizing the species calculus, to obtain a genuinely fermionic/super Fock structure?

Cool observation: one can build a bicategory whose objects are free word monoids over alphabets and whose morphisms are Turing transducers. A Turing machine then appears as a specialization of a guarded trace between a Moore machine (tape) and a Mealy machine (controller).

Formally speaking: Given a type system and an operational semantics, what more is needed for a 'meaning explanation'?

Looking for non-trivial examples of virtual double categories arising in TCS or logic, ideally many-object examples where the virtuality has a concrete computational/logical meaning.

I was reading the Day-Street paper on Quantum Categories over the weekend and in the introduction they mention a hope of interaction between linear logic and quantum group theory, but I haven't been able to find much progress on this, does anyone know of any references on this?

after two years of development, I finally demoed Jermaine for the first time - a language with fully symmetric data and codata, and native call-cc.

For the past few months, I’ve been working on a personal research project, *Categorical Automata Theory*. The first volume, *Residual Behaviour and Operational Algebra*, is still a work in progress, but it’s now at a stage I’m happy to share: github.com/uzum4ke/Auto...

In favourable settings, a linear exponential modality admits a free differential completion, yielding a model of differential linear logic. Operads and related algebraic theories also admit deformation theory. Is there a translation between these constructions?