Applied Category Theory 2021 — Adjoint School

2 January, 2021

Do you want to get involved in applied category theory? Are you willing to do a lot of work and learn a lot? Then this is for you:

Applied Category Theory 2021 — Adjoint School. Applications due Friday 29 January 2021. Organized by David Jaz Myers, Sophie Libkind, and Brendan Fong.

There are four projects to work on with great mentors. You can see descriptions of them below!

By the way, it’s not yet clear if there will be an in-person component to this school —but if there is, it will happen at the University of Cambridge. ACT2021 is being organized by Jamie Vicary, who teaches in the computer science department there.

Who should apply?

Anyone, from anywhere in the world, who is interested in applying category-theoretic methods to problems outside of pure mathematics. This is emphatically not restricted to math students, but one should be comfortable working with mathematics. Knowledge of basic category-theoretic language—the definition of monoidal category for example—is encouraged.

We will consider advanced undergraduates, PhD students, post-docs, as well as people working outside of academia. Members of groups which are underrepresented in the mathematics and computer science communities are especially encouraged to apply.

School overview

Participants are divided into four-person project teams. Each project is guided by a mentor and a TA. The Adjoint School has two main components: an Online Seminar that meets regularly between February and June, and an in-person Research Week in Cambridge, UK on July 5–9.

During the online seminar, we will read, discuss, and respond to papers chosen by the project mentors. Every other week, a pair of participants will present a paper which will be followed by a group discussion. Leading up to this presentation, study groups will meet to digest the reading in progress, and students will submit reading responses. After the presentation, the presenters will summarize the paper into a blog post for The n-Category Cafe.

The in-person research week will be held the week prior to the International Conference on Applied Category Theory and in the same location. During the week, participants work intensively with their research group under the guidance of their mentor. Projects from the Adjoint School will be presented during this conference. Both components of the school aim to develop a sense of belonging and camaraderie in students so that they can fully participate in the conference, for example by attending talks and chatting with other conference goers.

Projects to choose from

Here are the projects.

Topic: Categorical and computational aspects of C-sets

Mentors: James Fairbanks and Evan Patterson

Description: Applied category theory includes major threads of inquiry into monoidal categories and hypergraph categories for describing systems in terms of processes or networks of interacting components. Structured cospans are an important class of hypergraph categories. For example, Petri net-structured cospans are models of concurrent processes in chemistry, epidemiology, and computer science. When the structured cospans are given by C-sets (also known as co-presheaves), generic software can be implemented using the mathematics of functor categories. We will study mathematical and computational aspects of these categorical constructions, as well as applications to scientific computing.

Readings:

Structured cospans, Baez and Courser.

An algebra of open dynamical systems on the operad of wiring diagrams, Vagner, Spivak, and Lerman.

Topic: The ubiquity of enriched profunctor nuclei

Mentor: Simon Willerton

Description: In 1964, Isbell developed a nice universal embedding for metric spaces: the tight span. In 1966, Isbell developed a duality for presheaves. These are both closely related to enriched profunctor nuclei, but the connection wasn’t spotted for 40 years. Since then, many constructions in mathematics have been observed to be enriched profunctor nuclei too, such as the fuzzy/formal concept lattice, tropical convex hull, and the Legendre–Fenchel transform. We’ll explore the world of enriched profunctor nuclei, perhaps seeking out further useful examples.

Readings:

The Legendre–Fenchel transform from a category theoretic perspective, Willerton.

On the fuzzy concept complex (chapters 2-3), Elliot.

Topic: Double categories in applied category theory

Mentor: Simona Paoli

Description: Bicategories and double categories (and their symmetric monoidal versions) have recently featured in applied category theory: for instance, structured cospans and decorated cospans have been used to model several examples, such as electric circuits, Petri nets and chemical reaction networks.

An approach to bicategories and double categories is available in higher category theory through models that do not require a direct checking of the coherence axioms, such as the Segal-type models. We aim to revisit the structures used in applications in the light of these approaches, in the hope to facilitate the construction of new examples of interest in applications.

Readings:

Structured cospans, Baez and Courser.

A double categorical model of weak 2-categories, Paoli and Pronk.

and introductory chapters of:

Simplicial Methods for Higher Categories: Segal-type Models of Weak n-Categories, Paoli.

Topic: Extensions of coalgebraic dynamic logic

Mentors: Helle Hvid Hansen and Clemens Kupke

Description: Coalgebra is a branch of category theory in which different types of state-based systems are studied in a uniform framework, parametric in an endofunctor F:C → C that specifies the system type. Many of the systems that arise in computer science, including deterministic/nondeterministic/weighted/probabilistic automata, labelled transition systems, Markov chains, Kripke models and neighbourhood structures, can be modeled as F-coalgebras. Once we recognise that a class of systems are coalgebras, we obtain general coalgebraic notions of morphism, bisimulation, coinduction and observable behaviour.

Modal logics are well-known formalisms for specifying properties of state-based systems, and one of the central contributions of coalgebra has been to show that modal logics for coalgebras can be developed in the general parametric setting, and many results can be proved at the abstract level of coalgebras. This area is called coalgebraic modal logic.

In this project, we will focus on coalgebraic dynamic logic, a coalgebraic framework that encompasses Propositional Dynamic Logic (PDL) and Parikh’s Game Logic. The aim is to extend coalgebraic dynamic logic to system types with probabilities. As a concrete starting point, we aim to give a coalgebraic account of stochastic game logic, and apply the coalgebraic framework to prove new expressiveness and completeness results.

Participants in this project would ideally have some prior knowledge of modal logic and PDL, as well as some familiarity with monads.

Readings:

Parts of these:

Universal coalgebra: a theory of systems, Rutten.

Coalgebraic semantics of modal logics: an overview, Kupke and Pattinson.

Strong completeness of iteration-free coalgebraic dynamic logics, Hansen, Kupke, and Leale.


Graph Transformation Theory and Applications

4 December, 2020

I love graph rewriting—the study of ways to change one graph into another by changing one small part at a time. My student Daniel Cicala did his thesis on this! So I’m happy to hear about the new virtual seminar series GReTA: Graph TRansformation Theory and Applications.

It aims to serve as a platform for the international graph rewriting community, promote recent developments and trends in the field, and encourage regular networking and interaction between members of this community.

Seminars are held twice a month in the form of Zoom sessions (some of which will be live-streamed to YouTube). Go to the link if you want to join on Zoom.

You can get regular updates on the GReTA seminars in several ways:

• Subscribe to the GReTA YouTube channel.

• Subscribe to the GReTA Google Calendar (or alternatively import it in iCal format).

• Subscribe to the GReTA mailing list.

Here are the two talks so far. Any subject that can promote talks on both logic and chemistry must be good! Thinking of chemistry and logic as two aspects of the same thing is bound to trigger new ideas. (Just as a sequence of chemical reactions converts reactants into products, a proof converts assumptions into conclusions.)

Speaker: Barbara König
Title: Graph transformation meets logic

Abstract. We review the integration of (first-order) logic respectively nested conditions into graph transformation. Conditions can serve various purposes: they can constrain graph rewriting, symbolically specify sets of graphs, be used in query languages and in verification (for instance in Hoare logic and for behavioural equivalence checking). In the graph transformation community the formalism of nested graph conditions has emerged, that is, conditions which are equivalent to first-order logic, but directly integrate graphs and graph morphisms, in order to express constraints more succinctly. In this talk we also explain how the notion of nested conditions can be lifted from graph transformation systems to the setting of reactive systems as defined by Leifer and Milner. It turns out that some constructions for graph transformation systems (such as computing weakest preconditions and strongest postconditions and showing local confluence by means of critical pair analysis) can be done quite elegantly in the more general setting.

Speakers: Daniel Merkle and Jakob Lykke Andersen
Title: Chemical graph transformation and applications

Abstract: Any computational method in chemistry must choose some level of precision in the modeling. One choice is made in the methods of quantum chemistry based on quantum field theory. While highly accurate, the methods are computationally very demanding, which restricts their practical use to single reactions of molecules of moderate size even when run on supercomputers. At the same time, most existing computational methods for systems chemistry and biology are formulated at the other abstraction extreme, in which the structure of molecules is represented either not at all or in a very rudimentary fashion that does not permit the tracking of individual atoms across a series of reactions.

In this talk, we present our on-going work on creating a practical modelling framework for chemistry based on Double Pushout graph transformation, and how it can be applied to analyse chemical systems. We will address important technical design decisions as well as the importance of methods inspired from Algorithm Engineering in order to reach the required efficiency of our implementation. We will present chemically relevant features that our framework provides (e.g. automatic atom tracing) as well as a set of chemical systems we investigated are currently investigating. If time allows we will discuss variations of graph transformation rule compositions and their chemical validity.


ACT2020 Program

27 June, 2020

Boston2

Applied Category Theory 2020 is coming up soon! After the Tutorial Day on Sunday July 6th, there will be talks from Monday July 7th to Friday July 10th. All talks will be live on Zoom and on YouTube. Recorded versions will appear on YouTube later.

Here is the program—click on it to download a more readable version:


Here are the talks! They come in three kinds: keynotes, regular presentations and short industry presentations. Within each I’ve listed them in alphabetical order by speaker: I believe the first author is the speaker.

This is gonna be fun.

Keynote presentations (35 minutes)

• Henry Adams, Johnathan Bush and Joshua Mirth, Operations on metric thickenings.

• Nicolas Blanco and Noam Zeilberger: Bifibrations of polycategories and classical linear logic.

• Bryce Clarke, Derek Elkins, Jeremy Gibbons, Fosco Loregian, Bartosz Milewski, Emily Pillmore and Mario Román: Profunctor optics, a categorical update.

• Tobias Fritz, Tomáš Gonda, Paolo Perrone and Eigil Rischel: Distribution functors, second-order stochastic dominance and the Blackwell–Sherman–Stein Theorem in categorical probability.

• Micah Halter, Evan Patterson, Andrew Baas and James Fairbanks: Compositional scientific computing with Catlab and SemanticModels.

• Joachim Kock: Whole-grain Petri nets and processes.

• Andre Kornell, Bert Lindenhovius and Michael Mislove: Quantum CPOs.

• Martha Lewis: Towards logical negation in compositional distributional semantics.

• Jade Master and John Baez: Open Petri nets.

• Lachlan McPheat, Mehrnoosh Sadrzadeh, Hadi Wazni and Gijs Wijnholds, Categorical vector space semantics for Lambek calculus with a relevant modality.

• David Jaz Myers: Double categories of open dynamical systems.

• Toby St Clere Smithe, Cyber Kittens, or first steps towards categorical cybernetics.

Regular presentations (20 minutes)

• Robert Atkey, Bruno Gavranović, Neil Ghani, Clemens Kupke, Jeremy Ledent and Fredrik Nordvall Forsberg: Compositional game theory, compositionally.

• John Baez and Kenny Courser: Coarse-graining open Markov processes.

• Georgios Bakirtzis, Christina Vasilakopoulou and Cody Fleming, Compositional cyber-physical systems modeling.

• Marco Benini, Marco Perin, Alexander Alexander Schenkel and Lukas Woike: Categorification of algebraic quantum field theories.

• Daniel Cicala: Rewriting structured cospans.

• Bryce Clarke: A diagrammatic approach to symmetric lenses.

• Bob Coecke, Giovanni de Felice, Konstantinos Meichanetzidis, Alexis Toumi, Stefano Gogioso and Nicolo Chiappori: Quantum natural language processing.

• Geoffrey Cruttwell, Jonathan Gallagher and Dorette Pronk: Categorical semantics of a simple differential programming language.

• Swaraj Dash and Sam Staton: A monad for probabilistic point processes.

• Giovanni de Felice, Elena Di Lavore, Mario Román and Alexis Toumi: Functorial language games for question answering.

• Giovanni de Felice, Alexis Toumi and Bob Coecke: DisCoPy: monoidal categories in Python.

• Brendan Fong, David Jaz Myers and David I. Spivak: Behavioral mereology: a modal logic for passing constraints.

• Rocco Gangle, Gianluca Caterina and Fernando Tohme, A generic figures reconstruction of Peirce’s existential graphs (alpha).

• Jules Hedges and Philipp Zahn: Open games in practice.

• Jules Hedges: Non-compositionality in categorical systems theory.

• Michael Johnson and Robert Rosebrugh, The more legs the merrier: A new composition for symmetric (multi-)lenses.

• Joe Moeller, John Baez and John Foley: Petri nets with catalysts.

• John Nolan and Spencer Breiner, Symmetric monoidal categories with attributes.

• Joseph Razavi and Andrea Schalk: Gandy machines made easy via category theory.

• Callum Reader: Measures and enriched categories.

• Mario Román: Open diagrams via coend calculus.

• Luigi Santocanale, Dualizing sup-preserving endomaps of a complete lattice.

• Dan Shiebler: Categorical stochastic processes and likelihood.

• Richard Statman, Products in a category with only one object.

• David I. Spivak: Poly: An abundant categorical setting for mode-dependent dynamics.

• Christine Tasson and Martin Hyland, The linear-non-linear substitution 2-monad.

• Tarmo Uustalu, Niccolò Veltri and Noam Zeilberger: Proof theory of partially normal skew monoidal categories.

• Dmitry Vagner, David I. Spivak and Evan Patterson: Wiring diagrams as normal forms for computing in symmetric monoidal categories.

• Matthew Wilson, James Hefford, Guillaume Boisseau and Vincent Wang: The safari of update structures: visiting the lens and quantum enclosures.

• Paul Wilson and Fabio Zanasi: Reverse derivative ascent: a categorical approach to learning Boolean circuits.

• Vladimir Zamdzhiev: Computational adequacy for substructural lambda calculi.

• Gioele Zardini, David I. Spivak, Andrea Censi and Emilio Frazzoli: A compositional sheaf-theoretic framework for event-based systems.

Industry presentations (8 minutes)

• Arquimedes Canedo (Siemens Corporate Technology).

• Brendan Fong (Topos Institute).

• Jelle Herold (Statebox): Industrial strength CT.

• Steve Huntsman (BAE): Inhabiting the value proposition for category theory.

• Ilyas Khan (Cambridge Quantum Computing).

• Alan Ransil (Protocol Labs): Compositional data structures for the decentralized web.

• Alberto Speranzon (Honeywell).

• Ryan Wisnesky (Conexus): Categorical informatics at scale.


ACT2020 Tutorial Day

17 June, 2020

If you’re wanting to learn some applied category theory, register for the tutorials that are taking place on July 5, 2020 as part of ACT2020!

Applied category theory offers a rigorous mathematical language and toolset for relating different concepts from across math, science, and technology. For example, category theory finds common patterns between geometry (shapes), algebra (equations), numbers, logic, probability, etc. Applied category theory (ACT) looks for how those very same patterns extend outward to data, programs, processes, physics, linguistics, and so on—things we see in the real world. The field is currently growing, as new applications and common patterns are being found all the time. When you understand these ideas, more of your intuitions about the world can be made rigorous and thus be communicated at a larger scale. This in turn gives our community a chance to solve larger and more complex scientific, technological, and maybe even societal problems.

This year’s international applied category theory conference ACT2020 is having a tutorial day, meant to introduce newcomers to applied category theory. Tutorial day will take place on July 5 and will include a few main topics that will be taught semi-traditionally (via presentation, exercises, and discussion) over Zoom, as well as mentors who will be available throughout the day to work with smaller groups and/or individuals. We invite you to sign up here if you’re interested, so we can keep you posted. Hope to see you there!

The four courses will be roughly as follows:

• David Spivak: categorical databases for introducing sets, functions, categories, and functors.

• Fabrizio Genovese: string diagrams as a graphical language for category theory.

• Emily Riehl: the Yoneda lemma in the context of matrices.

• Paolo Perrone: monads and comonads.


Applied Category Theory 2020 (Part 2)

23 March, 2020

Due to the coronavirus outbreak, many universities are moving activities online. This is a great opportunity to open up ACT2020 to a broader audience, with speakers from around the world.

The conference will take place July 6-10 online, coordinated by organizers in Boston USA. Each day there will be around six hours of live talks, which will be a bit more spaced out than usual to accommodate the different time zones of our speakers. All the talks will be both live streamed and recorded on YouTube. We will also have chat rooms and video chats in which participants can discuss various themes in applied category theory.

We will give more details as they become available and post updates on our official webpage:

http://act2020.mit.edu

Since there is no need to book travel, we were able to postpone the acceptance notification, and hence the submission deadline. If you would like to speak, please prepare an abstract or a conference paper according to the instructions here:

http://act2020.mit.edu/#papers

Important dates (all in 2020)

• Submission of contributed papers: May 10
• Acceptance/Rejection notification: June 7
• Tutorial day: July 5
• Main conference: July 6-10

Registration will now be free; please register for the conference ahead of time here:

http://act2020.mit.edu/#registration

We will send registering participants links to the live stream, the recordings, and the chat rooms, and we’ll use the list to inform participants of any changes.

Submissions

To give a talk at ACT2020, you have to submit a paper. You can submit either original research papers or extended abstracts of work submitted/accepted/published elsewhere. Accepted original research papers will be invited for publication in a proceedings volume.

Here’s how to submit papers. Two types of submissions are accepted, which will be reviewed to the same standards:

Proceedings Track. Original contributions of high quality work consisting of a 5–12 page extended abstract that provides evidence for results of genuine interest, and with enough detail to allow the program committee to assess the merits of the work. Submissions of works in progress are encouraged, but must be more substantial than a research proposal.

Non-Proceedings Track. Descriptions of high-quality work submitted or published elsewhere will also be considered, provided the work is recent and relevant to the conference. The work may be of any length, but the program committee members may only look at the first 3 pages of the submission, so you should ensure these pages contain sufficient evidence of the quality and rigor of your work.

Submissions should be prepared using LaTeX, and must be submitted in PDF format. Submission is currently open, and can be perfomed at the following web page:

https://easychair.org/conferences/?conf=act2020

One or more best paper awards may be given out at the discretion of the PC chairs. Selected contributions will be offered extended keynote slots in the program.

Organizers

Here are the local organizers:

• Destiny Chen (administration)
• Brendan Fong
• David Jaz Myers (logistics)
• Paolo Perrone (publicity)
• David Spivak

Here is the committee running the school:

• Carmen Constantin
• Eliana Lorch
• Paolo Perrone

Here is the steering committee:

• John Baez
• Bob Coecke
• David Spivak
• Christina Vasilakopoulou

Here is the program committee:

• Mathieu Anel, CMU
• John Baez, University of California, Riverside
• Richard Blute, University of Ottawa
• Tai-Danae Bradley, City University of New York
• Andrea Censi, ETC Zurich
• Bob Coecke, University of Oxford
• Valeria de Paiva, Samsung Research America and University of Birmingham
• Ross Duncan, University of Strathclyde
• Eric Finster, University of Birmingham
• Brendan Fong, Massachusetts Institute of Technology
• Tobias Fritz, Perimeter Institute for Theoretical Physics
• Richard Garner, Macquarie University
• Fabrizio Romano Genovese, Statebox
• Amar Hadzihasanovic, IRIF, Université de Paris
• Helle Hvid Hansen, Delft University of Technology
• Jules Hedges, Max Planck Institute for Mathematics in the Sciences
• Kathryn Hess Bellwald, Ecole Polytechnique Fédérale de Lausanne
• Chris Heunen, The University of Edinburgh
• Joachim Kock, UAB
• Tom Leinster, The University of Edinburgh
• Martha Lewis, University of Amsterdam
• Daniel R. Licata, Wesleyan University
• David Jaz Myers, Johns Hopkins University
• Paolo Perrone, MIT
• Vaughan Pratt, Stanford University
• Peter Selinger, Dalhousie University
• Michael Shulman, University of San Diego
David I. Spivak, MIT (co-chair)
• Walter Tholen, York University
• Todd Trimble, Western Connecticut State University
Jamie Vicary, University of Birmingham (co-chair)
• Maaike Zwart, University of Oxford


Applied Category Theory 2020 (Part 1)

1 March, 2020

Here’s the big annual conference on applied category theory:

ACT2020, 2020 July 6–10, online worldwide. Organized by Brendan Fong and David Spivak.

This happens right after the applied category theory school, which will take place June 29 – July 3. There will also be a tutorial day on Sunday July 5, with talks by Paolo Perrone, Emily Riehl, David Spivak and others.

To give a talk at ACT2020, you have to submit a paper. You can submit either original research papers or extended abstracts of work submitted/accepted/published elsewhere. Accepted original research papers will be invited for publication in a proceedings volume. Some contributions will be invited to become keynote addresses, and best paper awards may also be given. The conference will also include a business showcase.

Here’s how to submit papers. Two types of submissions are accepted, which will be reviewed to the same standards:

Proceedings Track. Original contributions of high quality work consisting of a 5–12 page extended abstract that provides evidence for results of genuine interest, and with enough detail to allow the program committee to assess the merits of the work. Submissions of works in progress are encouraged, but must be more substantial than a research proposal.

Non-Proceedings Track. Descriptions of high-quality work submitted or published elsewhere will also be considered, provided the work is recent and relevant to the conference. The work may be of any length, but the program committee members may only look at the first 3 pages of the submission, so you should ensure these pages contain sufficient evidence of the quality and rigor of your work.

Submissions should be prepared using LaTeX, and must be submitted in PDF format. Submission is currently open, and can be perfomed at the following web page:

https://easychair.org/conferences/?conf=act2020

Here are some important dates, all in 2020:

• Submission of contributed papers: April 26
• Acceptance/rejection notification: May 17
• Early bird registration deadline: May 20
• Final registration deadline: June 26
• Tutorial day: July 5
• Main conference: July 6–10

Here is the program committee:

• Mathieu Anel, CMU
• John Baez, University of California, Riverside
• Richard Blute, University of Ottawa
• Tai-Danae Bradley, City University of New York
• Andrea Censi, ETC Zurich
• Bob Coecke, University of Oxford
• Valeria de Paiva, Samsung Research America and University of Birmingham
• Ross Duncan, University of Strathclyde
• Eric Finster, University of Birmingham
• Brendan Fong, Massachusetts Institute of Technology
• Tobias Fritz, Perimeter Institute for Theoretical Physics
• Richard Garner, Macquarie University
• Fabrizio Romano Genovese, Statebox
• Amar Hadzihasanovic, IRIF, Université de Paris
• Helle Hvid Hansen, Delft University of Technology
• Jules Hedges, Max Planck Institute for Mathematics in the Sciences
• Kathryn Hess Bellwald, Ecole Polytechnique Fédérale de Lausanne
• Chris Heunen, The University of Edinburgh
• Joachim Kock, UAB
• Tom Leinster, The University of Edinburgh
• Martha Lewis, University of Amsterdam
• Daniel R. Licata, Wesleyan University
• David Jaz Myers, Johns Hopkins University
• Paolo Perrone, MIT
• Vaughan Pratt, Stanford University
• Peter Selinger, Dalhousie University
• Michael Shulman, University of San Diego
David I. Spivak, MIT (co-chair)
• Walter Tholen, York University
• Todd Trimble, Western Connecticut State University
Jamie Vicary, University of Birmingham (co-chair)
• Maaike Zwart, University of Oxford

Here is the steering committee:

• John Baez
• Bob Coecke
• David Spivak
• Christina Vasilakopoulou

Here is the committee running the school:

• Carmen Constantin
• Eliana Lorch
• Paolo Perrone

And here are the local organizers:

• Destiny Chen (administration)
• Brendan Fong
• David Jaz Myers (logistics)
• Paolo Perrone (publicity)
• David Spivak

More news will follow!


Applied Category Theory 2020 — Adjoint School

23 December, 2019

Boston2

Like last year and the year before, there will be a school associated to this year’s international conference on applied category theory! If you’re trying to get into applied category theory, this is the best possible way.

Applied Category Theory 2020 — Adjoint School.

The school will consist of online meetings from February to June 2020, followed by a research week June 29–July 3, 2020 at MIT in Cambridge Massachusetts. The conference follows on July 6–10, 2020, and if you attend the school you should also go to the conference.

The deadline to apply is January 15 2020; apply here.

There will be 4 mentors teaching courses at the school:

• Michael Johnson, Categories of maintainable relations.

• Nina Otter, Diagrammatic and algebraic approaches to distances between persistence modules.

• Valeria de Paiva, Dialectica categories of Petri nets.

• Michael Shulman, A practical type theory for symmetric monoidal categories.

Click on the links for more detailed information!

Who should apply?

Anyone, from anywhere in the world, who is interested in applying category-theoretic methods to problems outside of pure mathematics. This is emphatically not restricted to math students, but one should be comfortable working with mathematics. Knowledge of basic category-theoretic language—the definition of monoidal category for example—is encouraged.

We will consider advanced undergraduates, PhD students, post-docs, as well as people working outside of academia. Members of minorities, and of any groups which are underrepresented in the mathematics and computer science communities, are especially encouraged to apply.

Structure of the school

Every participant will be assigned to one of the groups above, according to their preference (and to the availability of places within the groups). Each group will consist of a mentor, a TA, and 4-5 students.

Online meetings

Between February and June 2020 there will be an online reading seminar. Each group will have a reading list of two papers, which they will study, and then present to the rest of the school during weekly online meetings. Every member of the school is encouraged to take part in the discussion of every paper, first during the meeting via live chat, and then, in written form, on an online forum. After the presentation and the forum discussion the students of each group will write a blog post about their assigned paper on the n-Category Café.

During this period, the TAs will be there to help the students, answer any question they might have, and moderate the discussions. This way, all the participants will build the necessary background to take part in the research activities during the week at MIT.

Research week

After the online meetings, there will be a two-week event at MIT, from June 29th to July 10th 2020. The first week is dedicated exclusively to the participants of the school. They will work in groups on the research projects outlined above, led by their mentors, with the help of their TAs.

During the second week the ACT 2020 Conference will take place, which is open to a wider audience. The member of each group of the school will have the possibility to present their activity to the audience of the conference, and share their ideas. The conference is not technically part of the school, but is about very similar topics, and participation is very much encouraged. The online meetings should prepare students to be able to follow some of the conference presentations to a reasonable degree, and introduce them to the main problems and techniques of the field.

Questions?

For any questions or doubts please write us at the address act adjoint school at gmail dot com.

Organizers

Carmen Constantin

Eliana Lorch

Paolo Perrone


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.