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!
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.
But before seeing what they wrote, I’d just like to point out that the final Topos Institute Colloquium of the year (the 9th of December) will be a bit special: there will be a short opening talk by Ilyas Khan, and then Robert Harper’s talk will be followed by a “town hall” session, led by Brendan. In this session, Brendan will talk a little bit about Topos in general, but, to do so, we would like to know what sorts of things you would like to hear about. So if you have a question or comment that you’d like us to respond to (or if you’d like to leave some feedback about events such as the colloquium), then you can head over to this (anonymous) Google form and let us know!
1 David
I’ve really enjoyed this past year with Topos, my first one fully employed here. I spent the first half of the year back in Boston, and then moved out in June to be with the team in person. The summer was fantastic, so lively with visitors. We had tons of great math and philosophy conversations, made all the better by dinners cooked by the house of grad students (David Jaz, Christian, Josh, Nelson, Sophie) were really fun. When the covid-delta variant hit and we all went home, it was a little sad. But slowly things have picked up again, and it’s great that the mask mandate has lifted. Hopefully the Berkeley seminar will start up again in a month or two.
I think the math this year has been great. I’ve been pushing the Poly stuff pretty hard, and feel proud of a couple accomplishments. One was putting artificial neural nets and interacting dynamical systems on the same footing; my paper with Tim on the subject has been getting some good interest from a variety of people. And the other was finally understanding database aggregation. Poly has just the right structures to let us define one of the most ubiquitous operations in the world (I am not basing this on facts I know, just intuition) using only universal properties and monoidal operations within Poly. Wanting to put aggregation alongside querying, playing together as they should, is a problem I’ve worked on for 12 years now, so I’m really excited to have made what I consider major progress in that area.
2 Valeria
2021 was a very difficult year for most of us: the pandemic which looked like it was receding in the Spring (at least it looked like that in California, when the vaccine became available) came back, showing that it hasn’t been tamed. Yet, we hope. But we mourn the thousands and thousands that were taken too soon. The economic crisis, brought about in part by the pandemic, is just starting to unfold. (Economics is always a few steps behind politics: it’s much harder to tell the numbers of deaths it causes.) The climatic crisis catastrophes, not as bad as they were in California in 2020, are still very much with us: we have droughts, wildfires, floods, you name it… Against this backdrop of suffering, it feels almost inconsiderate to think that I am working exactly on what I wanted to for so many years. It feels good to tell people that the Topos mission is to “shape technology for public benefit by advancing sciences of connection and integration”. And it is great to have similarly minded people to do it with! Topos is still starting, but we believe in community, diversity, equity and inclusion; and we’re working for that. The challenges are enormous: they go from curbing the arrogance of mathematicians and tech people who think they know how to do others’ work better than themselves, to convincing biologists, social scientists, and humanities researchers that we can bring something to the table, in a respectful manner. But if the challenges are considerable, the payoff is incredible. We hope not only “To invent the future” (as in a previous place), but to invent a just, sustainable and equitable future for us all. Thank you for all the joint work, friends!!
(missing pictures of Elaine Pimentel, Luiz Carlos Pereira, Samuel Gomes da Silva, Jacob Collard and Eswaran Subrahmanian).
3 Tish
As 2021 dawned, Topos Institute took shape and form as a viable and vibrant nonprofit institution led by David Spivak and Brendan Fong, and nurtured by a committed board and a community of mathematicians passionate about the power of category theory to provide a framework for addressing problems in a way that benefits humanity. I am neither a mathematician nor a philosopher: my greatest accomplishment of 2021 was in partnering with Brendan and David to bring my decades long experience in starting and running nonprofit research institutions to help envision the future and build the needed administrative and operating infrastructure that underpins everything that Topos does.
Topos began 2021 as a virtual organization, tied together by a common purpose, video meeting platforms, and a cadre of committed volunteers, and ended the year an overcrowded and productive physical space, with robust scientific interactions and achievements, and lively discussions (internally and externally) of how to organize our work and ourselves to facilitate public benefit. We still use video platforms and wear masks, but Topos has become the place we envisioned, both physically and intellectually.
As we near the solstice and look ahead to returning light there challenges for the new year include broadening our message, improving our communication and engaging more people in our mission and our work.
4 Brendan
Wow, it’s been one year of Topos! Or at least one year since David and I left MIT, and with Tish, Evan, Valeria, and Tim celebrated our formal opening by deciding we should have fortnightly ‘stand-up’ meetings. After spending a decade gradually figuring out how I might be a research mathematician, this year I’ve learned so much about things I never expected: health insurance law, accounting for indirect cost rates on government contracts, cheap strategies for furnishing an office, and designing hiring and interview processes.
But what it always comes down to is building a community that works together towards a common goal. A community of very diverse skills and roles, from doing basic science and technology research, yes, to thinking about the impacts of technology and the ethical roles of those who create it, to effectively sharing what we do with the world, to ensuring a robust organisation with healthy oversight. Growing this community during a pandemic has been an adventure — indeed, we’ve all had to work hard to maintain the existing communities so important to us — but it’s always humbling to see how the strength of the shared vision draws people together. It’s been a privilege to work with everyone in the Topos community — employees, volunteers, donors, advisors, our amazing board (thanks Ilyas, Ed, and Wesley!) — and I remain truly hopeful about the impact we can have on shaping technology for the public benefit through a new science of healthy systems.
While our community spans continents and relies on the vision of many people who have never even set foot in one of our offices, one precious, simple joy that stands out is simply having lunch together as a team. Sometimes we even eat outside.
5 Juliet
A little bit about me… My name is Juliet Szatko, and I am the Operations Assistant with Topos Institute. This last year, I have very much enjoyed getting acquainted with Topos’ administrative, accounting, governance, Human Resources, strategic and operational agendas. But my favorite thing about my role is how much I learn on a daily basis. Not only about the magic and mystery of the behind-the-scenes of non-profit research, or about the incredibly bright and brilliant natures of my team-members, but also about the rich world of category theory. I am inspired by the deeply meaningful connection that Topos draws between ethics and technology in its work and mission. Computational and mathematical innovation, that focuses on building systems for public-benefit, is at the heart of the just scientific practice this digital age demands. Moving forward, I hope to continue to grow from what I have learned and accomplish our far-reaching objectives to the best of my ability. I look forward to the future Topos Institute can bring about and I feel lucky to be a part of it! Cheers to a great year!
6 Sophie
At this time last year, I was just wading into Catlab and writing the first bits of code that would eventually become AlgebraicDynamics, a package in the AlgebraicJulia ecosystem for compositional dynamics. With the help of the AlgebraicJulia team, I’ve been delighted to bring to life my favorite mathematics in code and see it applied to various fields from cybernetics to epidemiology. 2021 also featured the fourth Adjoint School for applied category theory, which I co-organized with David Jaz Myers. With 4 projects and 18 students, we covered a lot of ground during the spring seminar, and the school culminated in a fantastic research week in July. A small group of Adjoint school participants were even able to gather at Topos for a great week of brainstorming at whiteboards and picnic lunches.
7 Evan
It has been a great privilege—not to mention a lot of fun—to work at the Topos Institute in its inaugural year. With other members of the AlgebraicJulia team, I wrote the first journal-length paper about Catlab, specifically our implementation of categorical databases as in-memory data structures generalizing graphs and data frames. For much of this year, I’ve worked with an interdisciplinary group of collaborators on a compositional approach to multiphysics simulations, based on the discrete exterior calculus (DEC) and category-theoretic diagrams. We’ll put out a few papers on this topic over the coming months, but in the meantime you can check out our implementation of the DEC on 2D semi-simplicial sets (triangular meshes) in CombinatorialSpaces. Most recently, in collaboration with David Spivak, I’ve been working on a very flexible form of data migration for categorical databases, based on categories on diagrams. A prototype implementation is already available in Catlab, and a blog post should be out by year end.
8 Toby
Well, 2021 has again been a year full of surprises, and despite its ups and downs, more of them have been of an optimistic variety. For me, the year began in Oxford and now unexpectedly ends in Glasgow: but throughout this time, it has been a great privilege to be part of the Topos community, dispersed as we have been; the Topos mission to achieve a new world of connection and integration never felt more fitting. It has been wonderful to see from afar (and in whatever spurts!) the Institute coming to life in Berkeley, and I hope that before long we see the same mathematical vibrancy and compassion springing forth in Topos campuses (subToposes?) in Europe and across the world.
For my part, the surprises have not just been geographical or biological, but mathematical, too; despite knowing a little of them, I had not expected at the beginning of the year to end it quite so enamoured with polynomial functors, nor to have spent quite so long thinking about open dynamical systems indexed by polynomials. But these gadgets are so versatile for organizing interacting systems that I expect to be working with them for some time to come, as I and others seek to understand the mathematics of complex living and cybernetic systems. And so, in the coming year (and amongst many other things), I hope we illuminate the relationships between ‘polynomial’ and ‘optical’ accounts of cybernetics; to continue my work on compositional active inference; and generally help Topos thrive and grow.
9 Tim
About a year and a half ago, I was melting in a heatwave the south of France while writing my PhD thesis on simplicial methods in complex-analytic geometry; I write this current paragraph sat looking out the window at the start of a cold Swedish winter, having just finished editing an article with David on deep neural networks and interacting dynamical systems. The (cliché) point is that life often diverges from whatever you had planned for it to do. In this case, however, I am happy with the way that things have changed: working with the people here at Topos (even virtually) has been a sincere joy.
My involvement with Topos has gotten deeper and deeper over this past year as I’ve realised how much the core goals of the institute align with my own personal values. Every time we hear about another global tech corporation abusing their power, see some new way of statistics being twisted and misapplied to push a political conspiracy, or advances in theoretical science being fed directly into military development of new weapons, we are prompted to reflect on what our responsibility as “mathematicians” really is. On a smaller scale, we must also ask what sort of environments we should be creating for the next generation of researchers, and how we can ensure that these environments accurately reflect the priorities that we value. To be blunt, I believe that this means, for example, taking DEI seriously, and not just paying it lip service; a “traditional” goal like “publishing maths in top journals” should rank severely below something like “ensuring that our research teams really do represent the larger society around us, with their members actually being listened to”.
