Tim Hosgood

Director of UK Operations

Topos UK

Although my main mathematical research focuses on simplicial methods in geometry, I have a keen interest in understanding how we can use mathematics to make mathematics (and science, and knowledge in general) more accessible to all. Only by ensuring that we have, and give power to, a wide range of voices within our, and others’, communities can we truly hope to build technology that supports everybody, not just a select few.

Blog posts

DOTS from double theories

Working as a mathematician at Topos means that I spend a lot of time hearing about double categories these days, which are not something that I have much previous familiarity with. In fact, they come up in two seemingly different ways in Topos’ work at the moment: double theories, and double…

Tim Hosgood

2025-11-07

Open position: Director of UK Operations

Topos UK is hiring for a Director of Operations. What does this mean? Read more to find out.

Tim Hosgood

2025-10-07

TopOx seminar

Next week we’re co-hosting an in-person seminar talk in Oxford. This post contains the mailing announcement.

Tim Hosgood

2025-05-08

Open curricula and assessment tools workshop in Kisumu

In August, Brendan and I attended the American Institute of Mathematics workshop “Open source mathematics curriculum and assessment tools”, hosted by Maseno University in Kisumu, Kenya. The workshop was a fantastic opportunity to meet new specialists in a variety of domains and hear about what…

Tim Hosgood

2024-09-06

Postdoc job openings in Topos Oxford, UK

Topos is opening its doors in Oxford, UK, and is inviting applications for two postdoctoral researchers to come work with us on one of our first projects.

Tim Hosgood

2024-08-30

Our Summer Research Associates in 2024

Another year, another cohort of wonderful Summer Research Associates (RAs) at Topos working on exciting projects. As is now the custom, we’ve asked each of them to introduce themselves and write a little bit about what they’ll be working on over the summer. You can expect to see some blog posts…

Tim Hosgood

2024-07-29

Understanding UMAP

UMAP is a dimension-reduction method that has become very popular, especially in many areas of biology. Recently, a certain figure produced by UMAP has been circulated online to support spurious conclusions about “genetic racial groups”, or, to put it more bluntly, to support scientific racism. In…

Tim Hosgood

2024-04-05

Diagrammatic equations and multiphysics (Part 2)

Previously, we surveyed some of the fundamental concepts from our paper on the use of diagrams to present equations from mathematical physics. In this blog post we take a look at how we can enrich our framework, introducing cartesian and symmetric monoidal products in order to be able to express…

Tim Hosgood, Evan Patterson

2022-04-15

Diagrammatic equations and multiphysics (Part 1)

Using diagrams to encode equations between physical quantities is something that has become more and more common over the past few decades. To a category theorist, however, the use of such diagrams is not as formal as one would perhaps like. In this new paper, we fix this problem: systematising…

Tim Hosgood, Evan Patterson

2022-04-08

Brits in Berkeley

Throughout the past calendar year, Topos Oxford has mostly comprised just two people: Toby St Clere Smithe and myself (Tim Hosgood). Since Berkeley has been the Topos site of initial focus, we’ve been working mostly remotely from the rest of the team. But last week was an exciting one for us all…

Tim Hosgood

2022-03-22

Topos Institute seminars in 2022

With a new calendar year comes a new seminar! On the 25th of January, our very own David Spivak will be giving the inaugural talk ("Categorical interaction in the polynomial ecosystem") of the Intercats seminar, and the seminars will then be held every other Tuesday at 17:00 UTC. The Topos…

Tim Hosgood

2022-01-07

Topos in 2021: a retrospective

As this calendar year draws to a close, I asked the members of Topos to each write a little bit about what they’ve worked on this year, how things have gone, and what plans they might have for the future. Here’s what they wrote!

Tim Hosgood

2021-12-02

Left adjoints, lenses, and localisation

In this post I am going to recount three stories that I’ve been thinking about recently: Cauchy completion, internal lenses, and GZ/zigzag-localisation. The first two of these stories are probably more likely to be familiar to the (applied) category theory audience of this blog than the third. For…

Tim Hosgood

2021-11-24

Deep neural networks as nested dynamical systems

This week, we (David Spivak and Tim Hosgood) uploaded a new paper to the arXiv: “Deep neural networks as nested dynamical systems”. In it, we discuss how to think of both deep neural networks and interacting dynamical systems as some encompassing generalisation, which we call deeply interactive…

Tim Hosgood, David Spivak

2021-11-05

Announcing Em-Cats

The Em-Cats seminar series that was announced a while back is almost about to start! We will be welcoming our first speaker (Jade Master) on Wednesday the 25th of August. Here is some more information about this opening talk.

Tim Hosgood

2021-08-24

Dirichlet polynomials and entropy

Recently, we (David Spivak and Tim Hosgood) put a preprint on the arXiv called “Dirichlet polynomials and entropy”, which explains how to recover Shannon entropy from a rig homomorphism involving the weighted geometric mean. In this blog post, we explain the main story, from a slightly different…

Tim Hosgood, David Spivak

2021-07-25

Seminars and workshops so far

Although this blog has only just launched, the Topos Institute has been running quite a few public-facing events over the past five months or so, including a workshop and regular seminar series. With even more on the horizon, let’s take a look at what has been, and will be, going on.

Tim Hosgood

2021-07-08