Uploaded November 2025 | Updated September 2026, 2 weeks ago
Topos Institute Colloquium, 13th of November 2025.
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The study of modal logic has witnessed tremendous development following the introduction of Kripke semantics. However, recent developments in programming languages and type theory have led to a second way of studying modalities, namely through their categorical semantics. We show how the two correspond.
Topos Institute Colloquium, 13th of November 2025.
———
The study of modal logic has witnessed tremendous development following the introduction of Kripke semantics. However, recent developments in programming languages and type theory have led to a second way of studying modalities, namely through their categorical semantics. We show how the two correspond.
![[Oxford Seminar] David Jaz Myers | Compositionality via 2-algebra](https://i.ytimg.com/vi/XXIaJ98SUik/mqdefault.jpg "[Oxford Seminar] David Jaz Myers | Compositionality via 2-algebra
Oxford Seminar, May 28 2026
Speaker: David Jaz Myers
Full Title: Compositionality via 2-algebra
Abstract: A complex system may be designed modularly by putting together interacting component subsystems. Since analyses of complex systems can often scale very poorly with their size, it pays to use the modular structure of such systems to divide the task of analysis across the component subsystems.
Many analyses of systems may be encoded as homomorphism search problems between systems of the same sort. This suggests attending to categories of systems and their homomorphisms. In this talk, well consider the modular structure of a class of systems as a 2-algebra — an algebraic structure on categories of systems (and their interfaces and interaction patterns). Well see compositionality theorems as (lax) homomorphisms of these 2-algebraic structures, and survey a number of techniques for proving them using 2-categorical algebra.")
![[DOTS Lectures] 8. Compositionality of behaviours: generalized Moore machine case](https://i.ytimg.com/vi/Xxo8Om-pBn8/mqdefault.jpg "[DOTS Lectures] 8. Compositionality of behaviours: generalized Moore machine case
Part of a lecture series on the Double Operadic Theory of Systems (DOTS) presented by David Jaz Myers.
Some material from these lectures can be found in Davids book on categorical systems theory:
https://www.davidjaz.com/Papers/DynamicalBook.pdf")
![[Oxford Seminar] Tim Hosgood | Homotopy coherent Bousfield–Kan](https://i.ytimg.com/vi/Y9w6YzhEaoo/mqdefault.jpg "[Oxford Seminar] Tim Hosgood | Homotopy coherent Bousfield–Kan
Oxford Seminar, July 30 2026
You can view the listing for this talk online at https://topos.institute/events/oxford-seminar/talks/2026-07-30_hosgood_bousfield.html
Speaker: Tim Hosgood
Full Title: Homotopy coherent Bousfield–Kan
Abstract: From a weird little-known construction in complex geometry we can notice a new type of subdivision of simplices: half cubical, half simplicial, and very useful for working with certain geometric objects. These subdivisions are called /homotopy-coherent simplices/ (previously /wiggly simplices/).
In this talk I will give an introduction to the theory and methodology of homotopy limits of cosimplicial spaces through some tools of 2-category theory, explaining the important construction of Bousfield–Kan, and how this generalises to the homotopy coherent setting following joint work with Jason Brown and Cheyne Glass. I will also show lots of pictures of triangles. If times permits, I will introduce the notion of /homotopy homotopy limit/.
/Prerequisites./ The talk will use Quillen model categories and cosimplicial simplicial sets, but I will try to give good enough speedy overviews of both of these definitions. I will also use some definitions from enriched category theory (namely weighted (co)limits) but in a way that will likely make any Australians in the room rather upset.
/Recommended pre-reading./ The following definitions: nerve of a category, barycentric subdivision of a simplex, simplicial set.")
![[Berkeley Seminar] Mike Dodds (Galois) | What works and doesnt selling formal methods in industry](https://i.ytimg.com/vi/Z2bTpsO4fcc/mqdefault.jpg "[Berkeley Seminar] Mike Dodds (Galois) | What works and doesnt selling formal methods in industry
Title: What works and doesnt selling formal methods in industry
Abstract:I joined Galois to do research, but to my surprise I also learned how to sell formal methods to industry and government. In this talk I will explain what I think works, what doesn’t, and what it says about formal methods as a technology. The spoiler is that clients are rational, formal methods are expensive, and this makes most potential projects unviable. As SPECIAL BONUS CONTENT I will also talk about AI and why it will probably change everything.
Date: November 10, 2025")
![[Oxford Seminar] Greg Neustroev | The Treachery of Certificates: Ceci n’est pas une supermartingale](https://i.ytimg.com/vi/ZO7KmOXGX98/mqdefault.jpg "[Oxford Seminar] Greg Neustroev | The Treachery of Certificates: Ceci n’est pas une supermartingale
Oxford Seminar, June 25 2026
You can view the listing for this talk online at https://topos.institute/events/oxford-seminar/talks/2026-06-25_neustroev_treachery.html
Speaker: Greg Neustroev
Full Title: The Treachery of Certificates: Ceci n’est pas une supermartingale
Abstract: To prove that a stochastic system exhibits a desired behavior with high probability (for example, that it reaches a target while avoiding danger) it often suffices to produce a single function on its states satisfying a few pointwise inequalities: a supermartingale certificate. Finding such a function is the hard part; checking one is easy, which is why neural networks, as flexible function-searchers, have become a natural tool for the job.
But a certificate is a static object — a function you can write down — while the object that actually carries the proof is a stochastic process: its dynamic interpretation as it rides the systems randomness. These are not the same thing, and the passage between them is not canonical: one function can induce many supermartingales, depending on how we stop, shift, or time-compensate it. Well build both objects from scratch, make the construction explicit, and see why conflating them — a common slip, even among practitioners — is exactly where soundness is won or lost.")
