Applied Category Theory Meeting at UCR (Part 3)

15 November, 2019


We had a special session on applied category theory here at UCR:

Applied category theory, Fall Western Sectional Meeting of the AMS, 9–10 November 2019, U.C. Riverside.

I was bowled over by the large number of cool ideas. I’ll have to blog about some of them. A bunch of people stayed for a few days afterwards, and we had lots of great conversations.

The biggest news was that Brendan Fong and David Spivak definitely want to set up an applied category theory in the San Francisco Bay Area, which they’re calling the Topos Institute. They are now in the process of raising funds for this institute! I plan to be involved, so I’ll be saying more about this later.

But back to the talks. We didn’t make videos, but here are the slides. Click on talk titles to see abstracts of the talks. For a multi-author talk, the person whose name is in boldface is the one who gave the talk. You also might enjoy comparing the 2017 talks.

Saturday November 9, 2019

8:00 a.m.
Fibrations as generalized lens categoriestalk slides.
David I. Spivak, Massachusetts Institute of Technology

9:00 a.m.
Supplying bells and whistles in symmetric monoidal categoriestalk slides.
Brendan Fong, Massachusetts Institute of Technology
David I. Spivak, Massachusetts Institute of Technology

9:30 a.m.
Right adjoints to operadic restriction functorstalk slides.
Philip Hackney, University of Louisiana at Lafayette
Gabriel C. Drummond-Cole, IBS Center for Geometry and Physics

10:00 a.m.
Duality of relationstalk slides.
Alexander Kurz, Chapman University

10:30 a.m.
A synthetic approach to stochastic maps, conditional independence, and theorems on sufficient statisticstalk slides.
Tobias Fritz, Perimeter Institute for Theoretical Physics

3:00 p.m.
Constructing symmetric monoidal bicategories functoriallytalk slides.
Michael Shulman, University of San Diego
Linde Wester Hansen, University of Oxford

3:30 p.m.
Structured cospanstalk slides.
Kenny Courser, University of California, Riverside
John C. Baez, University of California, Riverside

4:00 p.m.
Generalized Petri netstalk slides.
Jade Master, University of California, Riverside

4:30 p.m.
Formal composition of hybrid systemstalk slides and website.

Paul Gustafson, Wright State University
Jared Culbertson, Air Force Research Laboratory
Dan Koditschek, University of Pennsylvania
Peter Stiller, Texas A&M University

5:00 p.m.
Strings for cartesian bicategoriestalk slides.
M. Andrew Moshier, Chapman University

5:30 p.m.
Defining and programming generic compositions in symmetric monoidal categoriestalk slides.
Dmitry Vagner, Los Angeles, CA

Sunday November 10, 2019

8:00 a.m.
Mathematics for second quantum revolutiontalk slides.
Zhenghan Wang, UCSB and Microsoft Station Q

9:00 a.m.
A compositional and statistical approach to natural languagetalk slides.
Tai-Danae Bradley, CUNY Graduate Center

9:30 a.m.
Exploring invariant structure in neural activity with applied topology and category theorytalk slides.
Brad Theilman, UC San Diego
Krista Perks, UC San Diego
Timothy Q Gentner, UC San Diego

10:00 a.m.
Of monks, lawyers and villages: new insights in social network science — talk cancelled due to illness.
Nina Otter, Mathematics Department, UCLA
Mason A. Porter, Mathematics Department, UCLA

10:30 a.m.
Functorial cluster embeddingtalk slides.

Steve Huntsman, BAE Systems FAST Labs

2:00 p.m.
Quantitative equational logictalk slides.
Prakash Panangaden, School of Computer Science, McGill University
Radu Mardare, Strathclyde University
Gordon D. Plotkin, University of Edinburgh

3:00 p.m.
Brakes: an example of applied category theorytalk slides in PDF and Powerpoint.
Eswaran Subrahmanian, Carnegie Mellon University / National Institute of Standards and Technology

3:30 p.m.
Intuitive robotic programming using string diagramstalk slides.
Blake S. Pollard, National Institute of Standards and Technology

4:00 p.m.
Metrics on functor categoriestalk slides.
Vin de Silva, Department of Mathematics, Pomona College

4:30 p.m.
Hausdorff and Wasserstein metrics on graphs and other structured datatalk slides.
Evan Patterson, Stanford University

Diversity Workshop at UCR

14 October, 2019

We’re having a workshop to promote diversity in math here at UCR:

Riverside Mathematics Workshop for Excellence and Diversity, Friday 8 November 2019, U. C. Riverside. Organized by John Baez, Weitao Chen, Edray Goins, Ami Radunskaya, and Fred Wilhelm.

If you want to come, please register here.

It’s happening right before the applied category theory meeting, so I hope some of you can make both… especially since the category theorist Eugenia Cheng will be giving a talk!

Three talks will take place in Skye Hall—home of the math department—starting at 1 pm. After this we’ll have refreshments and an hour for students to talk to the speakers. Starting at 6 pm there will be a reception across the road at the UCR Alumni Center, with food and a panel discussion on the challenges we face in promoting diversity at U.C. Riverside.

All the talks will be in Skye 284:

• 1:00–1:50 p.m. Abba Gumel, Arizona State University.

Some models for enhancing diversity and capacity-building in STEM education in under-represented minority communities.

STEM (science, technology, engineering and mathematics) education is undoubtedly the necessary bedrock for the development and sustenance of the vitally-needed knowledge-based economy that fuels and sustains the development of modern nations. Central to STEM education are, of course, the mathematical science … which are the rock-solid foundation of all the natural and engineering sciences. Hence, it is vital that all diverse populations are not left behind in the quest to build and sustain capacity in the mathematical sciences. This talk focuses on discussion around a number of pedagogic and mentorship models that have been (and are being) used to help increase diversity and capacity-building in STEM education in general, and in the mathematical sciences in particular, in under-represented minority populations. Some examples from Africa, Canada and the U.S. will be presented.

• 2:00–2:50. Marissa Loving, Georgia Tech.

Where do I belong? Creating space in the math community.

I will tell the story of my mathematical journey with a focus on my time in grad school. I will be blunt about the ups and downs I have experienced and touch on some of the barriers (both structural and internalized) I have encountered. I will also discuss some of the programs and spaces I have helped create in my quest to make the mathematics community into a place where folks from historically under-represented groups (particularly women of color) can feel safe, seen, and free to devote their energy to their work. If you have ever felt like you don’t belong or worried that you have made others feel that way, this talk is for you.

• 3:00–3:50 p.m. Eugenia Cheng, School of the Art Institute of Chicago.

Inclusion–exclusion in mathematics and beyond: who stays in, who falls out, why it happens, and what we could do about it.

The question of why women and minorities are under-represented in mathematics is complex and there are no simple answers, only many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives “ingressive” and “congressive” as a new dimension to shift our focus away from masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women. Moreover I will show that abstract mathematics is applicable to working towards a more inclusive, congressive society in this politically divisive era. This goes against the assumption that abstract math can only be taught to high level undergraduates and graduate students, and the accusation that it is removed from real life.

• 4:00–4:30 p.m. Refreshments in Skye 284.

• 4:30–5:30 p.m. Conversations Between Speakers & Students, Not Faculty, in Skye 284.

• 6:00–6:45 p.m. Reception with Food at the Alumni Center.

• 6:45 – 7:45 p.m. Panel Discussion at Alumni Center with Alissa Crans, Jose Gonzalez and Paige Helms, moderated by Edray Goins.

Applied Category Theory Meeting at UCR (Part 2)

30 September, 2019


Joe Moeller and I have finalized the schedule of our meeting on applied category theory:

Applied Category Theory, special session of the Fall Western Sectional Meeting of the AMS, U. C. Riverside, Riverside, California, 9–10 November 2019.

It’s going to be really cool, with talks on everything from brakes to bicategories, from quantum physics to social networks, and more—with the power of category theory as the unifying theme!

You can get information on registration, hotels and such here. If you’re coming, you might also want to attend Eugenia Cheng‘s talk on the afternoon of Friday November 8th.   I’ll announce the precise title and time of her talk, and also the location of all the following talks, as soon as I know!

In what follows, the person actually giving the talk has an asterisk by their name. You can click on talk titles to see abstracts of the talks.

Saturday November 9, 2019, 8:00 a.m.-10:50 a.m.

Saturday November 9, 2019, 3:00 p.m.-5:50 p.m.

Sunday November 10, 2019, 8:00 a.m.-10:50 a.m.

Sunday November 10, 2019, 2:00 p.m.-4:50 p.m.

2020 Category Theory Conferences

9 August, 2019


Yes, my last post was about ACT2019, but we’re already planning next year’s applied category theory conference and school! I’m happy to say that Brendan Fong and David Spivak have volunteered to run it at MIT on these dates:

• Applied Category Theory School: June 29–July 3, 2020.
• Applied Category Theory Conference: July 6–10, 2020.

The precise dates for the other big category theory conference, CT2020, have not yet been decided. However, it will take place in Genoa sometime in the interval June 18–28, 2020.

There may also be an additional applied theory school in Marrakesh from May 25–29, 2020. More on that later, with any luck!

And don’t forget to submit your abstracts for the November 2019 applied category theory special session at U. C. Riverside by September 3rd! We’ve got a great lineup of speakers, but anyone who wants to give a talk—including the invited speakers—needs to submit an abstract to the AMS website by September 3rd. The AMS has no mercy about this.

Applied Category Theory 2019 Talks

20 July, 2019

Applied Category Theory 2019 happened last week! It was very exciting: about 120 people attended, and they’re pushing forward to apply category theory in many different directions. The topics ranged from ultra-abstract to ultra-concrete, sometimes in the same talk.

The talks are listed above — click for a more readable version. Below you can read what Jules Hedges and I wrote about all those talks:

• Jules Hedges, Applied Category Theory 2019.

I tend to give terse summaries of the talks, with links to the original papers or slides. Jules tends to give his impressions of their overall significance. They’re nicely complementary.

You can also see videos of some talks, created by Jelle Herold with help from Fabrizio Genovese:

• Giovanni de Felice, Functorial question answering.

• Antonin Delpeuch, Autonomization of monoidal categories.

• Colin Zwanziger, Natural model semantics for comonadic and adjoint modal type theory.

• Nicholas Behr, Tracelets and tracelet analysis Of compositional rewriting systems.

• Dan Marsden, No-go theorems for distributive laws.

• Christian Williams, Enriched Lawvere theories for operational semantics.

• Walter Tholen, Approximate composition.

• Erwan Beurier, Interfacing biology, category theory & mathematical statistics.

• Stelios Tsampas, Categorical contextual reasoning.

• Fabrizio Genovese, idris-ct: A library to do category theory in Idris.

• Michael Johnson, Machine learning and bidirectional transformations.

• Bruno Gavranović, Learning functors using gradient descent

• Zinovy Diskin, Supervised learning as change propagation with delta lenses.

• Bryce Clarke, Internal lenses as functors and cofunctors.

• Ryan Wisnewsky, Conexus AI.

• Ross Duncan, Cambridge Quantum Computing.

• Beurier Erwan, Memoryless systems generate the class of all discrete systems.

• Blake Pollard, Compositional models for power systems.

• Martti Karvonen, A comonadic view of simulation and quantum resources.

• Quanlong Wang, ZX-Rules for 2-qubit Clifford+T quantum circuits, and beyond.

• James Fairbank, A Compositional framework for scientific model augmentation.

• Titoan Carette, Completeness of graphical languages for mixed state quantum mechanics.

• Antonin Delpeuch, A complete language for faceted dataflow languages.

• John van der Wetering, An effect-theoretic reconstruction of quantum mechanics.

• Vladimir Zamdzhiev, Inductive datatypes for quantum programming.

• Octavio Malherbe, A categorical construction for the computational definition of vector spaces.

• Vladimir Zamdzhiev, Mixed linear and non-linear recursive types.

Applied Category Theory 2019 Program

3 July, 2019

Bob Coecke, David Spivak, Christina Vasilakopoulou and I are running a conference on applied category theory:

Applied Category Theory 2019, 15–19 July, 2019, Lecture Theatre B of the Department of Computer Science, 10 Keble Road, Oxford.

You can now see the program here, or below. Hope to see you soon!

Applied Category Theory Meeting at UCR (Part 1)

16 June, 2019


The American Mathematical Society is having their Fall Western meeting here at U. C. Riverside during the weekend of November 9th and 10th, 2019. Joe Moeller and I are organizing a session on Applied Category Theory! We already have some great speakers lined up:

• Tai-Danae Bradley
• Vin de Silva
• Brendan Fong
• Nina Otter
• Evan Patterson
• Blake Pollard
• Prakash Panangaden
• David Spivak
• Brad Theilman
• Dmitry Vagner
• Zhenghan Wang

Alas, we have no funds for travel and lodging. If you’re interested in giving a talk, please submit an abstract here:

General information about abstracts, American Mathematical Society.

More precisely, please read the information there and then click on the link on that page to submit an abstract. It should then magically fly through the aether to me! Abstracts are due September 3rd, but the sooner you submit one, the greater the chance that we’ll have space.

For the program of the whole conference, go here:

Fall Western Sectional Meeting, U. C. Riverside, Riverside, California, 9–10 November 2019.

I will also be running a special meeting on diversity and excellence in mathematics on Friday November 8th. There will be a banquet that evening, and at some point I’ll figure out how tickets for that will work.

We had a special session like this in 2017, and it’s fun to think about how things have evolved since then.

David Spivak had already written Category Theory for the Sciences, but more recently he’s written another book on applied category theory, Seven Sketches, with Brendan Fong. He already had a company, but now he’s helping run Conexus, which plans to award grants of up to $1.5 million to startups that use category theory (in exchange for equity). Proposals are due June 30th, by the way!

I guess Brendan Fong was already working with David Spivak at MIT in the fall of 2017, but since then they’ve written Seven Sketches and developed a graphical calculus for logic in regular categories. He’s also worked on a functorial approach to machine learning—and now he’s using category theory to unify learners and lenses.

Blake Pollard had just finished his Ph.D. work at U.C. Riverside back in 2018. He will now talk about his work with Spencer Breiner and Eswaran Subrahmanian at the National Institute of Standards and Technology, using category theory to help develop the “smart grid”—the decentralized power grid we need now. Above he’s talking to Brendan Fong at the Centre for Quantum Technologies, in Singapore. I think that’s where they first met.

Eswaran Subrahmanian will also be giving a talk this time! He works at NIST and Carnegie Mellon; he’s an engineer who specializes in using mathematics to help design smart networks and other complex systems.

Nina Otter was a grad student at Oxford in 2017, but now she’s at UCLA and the University of Leipzig. She worked with Ulrike Tillmann and Heather Harrington on stratifying multiparameter persistent homology, and is now working on a categorical formulation of positional and role analysis in social networks. Like Brendan, she’s on the executive board of the applied category theory journal Compositionality.

I first met Tai-Danae Bradley at ACT2018. Now she will talk about her work at Tunnel Technologies, a startup run by her advisor John Terilla. They model sequences—of letters from an alphabet, for instance—using quantum states and tensor networks.

Vin de Silva works on topological data analysis using persistent cohomology so he’ll probably talk about that. He’s studied the “interleaving distance” between persistence modules, using category theory to treat it and the Gromov-Hausdorff metric in the same setting. He came to the last meeting and it will be good to have him back.

Evan Patterson is a statistics grad student at Stanford. He’s worked on knowledge representation in bicategories of relations, and on teaching machines to understand data science code by the semantic enrichment of dataflow graphs. He too came to the last meeting.

Dmitry Vagner was also at the last meeting, where he spoke about his work with Spivak on open dynamical systems and the operad of wiring diagrams. He is now working on mathematically defining and implementing (in Idris) wiring diagrams for symmetric monoidal categories.

Prakash Panangaden has long been a leader in applied category theory, focused on semantics and logic for probabilistic systems and languages, machine learning, and quantum information theory.

Brad Theilman is a grad student in computational neuroscience at U.C. San Diego. I first met him at ACT2018. He’s using algebraic topology to design new techniques for quantifying the spatiotemporal structure of neural activity in the auditory regions of the brain of the European starling. (I bet you didn’t see those last two words coming!)

Last but not least, Zhenghan Wang works on condensed matter physics and modular tensor categories at U.C. Santa Barbara. At Microsoft’s Station Q, he is using this research to help design topological quantum computers.

In short: a lot has been happening in applied category theory, so it will be good to get together and talk about it!