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!


Quantum Physics and Logic 2019

4 June, 2019
open_petri_4

There’s another conference involving applied category theory at Chapman University!

• Quantum Physics and Logic 2019, June 9-14, 2019, Chapman University, Beckman Hall 404. Organized by Matthew Leifer, Lorenzo Catani, Justin Dressel, and Drew Moshier.

The QPL series started out being about quantum programming languages, but it later broadened its scope while keeping the same acronym. This conference series now covers quite a range of topics, including the category-theoretic study of physical systems. My students Kenny Courser, Jade Master and Joe Moeller will be speaking there, and I’ll talk about Kenny’s new work on structured cospans as a tool for studying open systems.

Program

The program is here.

Invited talks

• John Baez (UC Riverside), Structured cospans.

• Anna Pappa (University College London), Classical computing via quantum means.

• Joel Wallman (University of Waterloo), TBA.

Tutorials

• Ana Belen Sainz (Perimeter Institute), Bell nonlocality: correlations from principles.

• Quanlong Wang (University of Oxford) and KangFeng Ng (Radboud University), Completeness of the ZX calculus.


Symposium on Compositional Structures 4: Program

11 May, 2019

Here’s the program for this conference:

Symposium on Compositional Structures 4, 22–23 May, 2019, Chapman University, California. Organized by Alexander Kurz.

A lot of my students and collaborators are speaking here! The meeting will take place in Beckman Hall 101.

Wednesday May 22, 2019

• 10:30–11:30 — Registration.

• 11:30–12:30 — John Baez, “Props in Network Theory“.

• 12:30–1:00 — Jade Master, “Generalized Petri Nets”.

• 1:00–2:00 — Lunch.

• 2:00–2:30 — Christian Williams, “Enriched Lawvere Theories for Operational Semantics”.

• 2:30–3:00 — Kenny Courser, “Structured Cospans”.

• 3:00–3:30 — Daniel Cicala, “Rewriting Structured Cospans”.

• 3:30–4:00 — Break.

• 4:00–4:30 — Samuel Balco and Alexander Kurz, “Nominal String Diagrams”.

• 4:30–5:00 — Jeffrey Morton, “2-Group Actions and Double Categories”.

• 5:00–5:30 — Michael Shulman, “All (∞,1)-Toposes Have Strict Univalent Universes”.

• 5:30–6:30 — Reception.

Thursday May 23, 2019

• 9:30–10:30 — Nina Otter, “A Unified Framework for Equivalences in Social Networks”.

• 10:30–11:00 — Kohei Kishida, Soroush Rafiee Rad, Joshua Sack and Shengyang Zhong, “Categorical Equivalence between Orthocomplemented Quantales and Complete Orthomodular Lattices”.

• 11:00–11:30 — Break.

• 11:30–12:00 — Cole Comfort, “Circuit Relations for Real Stabilizers: Towards TOF+H”.

• 12:00–12:30 — Owen Biesel, “Duality for Algebras of the Connected Planar Wiring Diagrams Operad”.

• 12:30–1:00 — Joe Moeller and Christina Vasilakopoulou, “Monoidal Grothendieck Construction”.

• 1:00–2:00 — Lunch.

• 2:00–3:00 — Tobias Fritz, “Categorical Probability: Results and Challenges”.

• 3:00–3:30 — Harsh Beohar and Sebastian Küpper, “Bisimulation Maps in Presheaf Categories”.

• 3:30–4:00 — Break.

• 4:00–4:30 — Benjamin MacAdam, Jonathan Gallagher and Rory Lucyshyn-Wright, “Scalars in Tangent Categories”.

• 4:30–5:00 — Jonathan Gallagher, Benjamin MacAdam and Geoff Cruttwell, “Towards Formalizing and Extending Differential Programming via Tangent Categories”.

• 5:00–5:30 — David Sprunger and Shin-Ya Katsumata, “Differential Categories, Recurrent Neural Networks, and Machine Learning”.


Symposium on Compositional Structures 4

8 April, 2019

There’s yet another conference in this fast-paced series, and this time it’s in Southern California!

Symposium on Compositional Structures 4, 22–23 May, 2019, Chapman University, California. Organized by Alexander Kurz.

The Symposium on Compositional Structures (SYCO) is an interdisciplinary series of meetings aiming to support the growing community of researchers interested in the phenomenon of compositionality, from both applied and abstract perspectives, and in particular where category theory serves as a unifying common language.
The first SYCO was in September 2018, at the University of Birmingham. The second SYCO was in December 2018, at the University of Strathclyde. The third SYCO was in March 2019, at the University of Oxford. Each meeting attracted about 70 participants.

We welcome submissions from researchers across computer science, mathematics, physics, philosophy, and beyond, with the aim of fostering friendly discussion, disseminating new ideas, and spreading knowledge between fields. Submission is encouraged for both mature research and work in progress, and by both established academics and junior researchers, including students.

Submission is easy, with no format requirements or page restrictions. The meeting does not have proceedings, so work can be submitted even if it has been submitted or published elsewhere. Think creatively—you could submit a recent paper, or notes on work in progress, or even a recent Masters or PhD thesis.

While no list of topics could be exhaustive, SYCO welcomes submissions
with a compositional focus related to any of the following areas, in
particular from the perspective of category theory:

• logical methods in computer science, including classical and quantum programming, type theory, concurrency, natural language processing and machine learning;

• graphical calculi, including string diagrams, Petri nets and reaction networks;

• languages and frameworks, including process algebras, proof nets, type theory and game semantics;

• abstract algebra and pure category theory, including monoidal category theory, higher category theory, operads, polygraphs, and relationships to homotopy theory;

• quantum algebra, including quantum computation and representation theory;

• tools and techniques, including rewriting, formal proofs and proof assistants, and game theory;

• industrial applications, including case studies and real-world problem descriptions.

This new series aims to bring together the communities behind many previous successful events which have taken place over the last decade, including “Categories, Logic and Physics”, “Categories, Logic and Physics (Scotland)”, “Higher-Dimensional Rewriting and Applications”, “String Diagrams in Computation, Logic and Physics”, “Applied Category Theory”, “Simons Workshop on Compositionality”, and the “Peripatetic Seminar in Sheaves and Logic”.

SYCO will be a regular fixture in the academic calendar, running regularly throughout the year, and becoming over time a recognized venue for presentation and discussion of results in an informal and friendly atmosphere. To help create this community, and to avoid the need to make difficult choices between strong submissions, in the event that more good-quality submissions are received than can be accommodated in the timetable, the programme committee may choose to
defer some submissions to a future meeting, rather than reject them. This would be done based largely on submission order, giving an incentive for early submission, but would also take into account other requirements, such as ensuring a broad scientific programme. Deferred submissions can be re-submitted to any future SYCO meeting, where they would not need peer review, and where they would be prioritised for inclusion in the programme. This will allow us to ensure that speakers have enough time to present their ideas, without creating an unnecessarily competitive reviewing process. Meetings will be held sufficiently frequently to avoid a backlog of deferred papers.

Invited speakers

John Baez, University of California, Riverside: Props in network theory.

Tobias Fritz, Perimeter Institute for Theoretical Physics: Categorical probability: results and challenges.

Nina Otter, University of California, Los Angeles: A unified framework for equivalences in social networks.

Important dates

All times are anywhere-on-earth.

• Submission deadline: Wednesday 24 April 2019
• Author notification: Wednesday 1 May 2019
• Registration deadline: TBA
• Symposium dates: Wednesday 22 and Thursday 23 May 2019

Submission

Submission is by EasyChair, via the following link:

https://easychair.org/conferences/?conf=syco4

Submissions should present research results in sufficient detail to allow them to be properly considered by members of the programme committee, who will assess papers with regards to significance, clarity, correctness, and scope. We encourage the submission of work in progress, as well as mature results. There are no proceedings, so work can be submitted even if it has been previously published, or has been submitted for consideration elsewhere. There is no specific formatting requirement, and no page limit, although for long submissions authors should understand that reviewers may not be able to read the entire document in detail.

Programme Committee

• Miriam Backens, University of Oxford
• Ross Duncan, University of Strathclyde and Cambridge Quantum Computing
• Brendan Fong, Massachusetts Institute of Technology
• Stefano Gogioso, University of Oxford
• Amar Hadzihasanovic, Kyoto University
• Chris Heunen, University of Edinburgh
• Dominic Horsman, University of Grenoble
• Martti Karvonen, University of Edinburgh
• Kohei Kishida, Dalhousie University (chair)
• Andre Kornell, University of California, Davis
• Martha Lewis, University of Amsterdam
• Samuel Mimram, École Polytechnique
• Benjamin Musto, University of Oxford
• Nina Otter, University of California, Los Angeles
• Simona Paoli, University of Leicester
• Dorette Pronk, Dalhousie University
• Mehrnoosh Sadrzadeh, Queen Mary
• Pawel Sobocinski, University of Southampton
• Joshua Tan, University of Oxford
• Sean Tull, University of Oxford
• Dominic Verdon, University of Bristol
• Jamie Vicary, University of Birmingham and University of Oxford
• Maaike Zwart, University of Oxford


Applied Category Theory 2019

7 February, 2019

I hope to see you at this conference, which will occur right before the associated school meets in Oxford:

Applied Category Theory 2019, July 15-19, 2019, Oxford, UK.

Applied category theory is a topic of interest for a growing community of researchers, interested in studying systems of all sorts using category-theoretic tools. These systems are found in the natural sciences and social sciences, as well as in computer science, linguistics, and engineering. The background and experience of our members is as varied as the systems being studied. The goal of the ACT2019 Conference is to bring the majority of researchers in the field together and provide a platform for exposing the progress in the area. Both original research papers as well as extended abstracts of work submitted/accepted/published elsewhere will be considered.

There will be best paper award(s) and selected contributions will be awarded extended keynote slots.

The conference will include a business showcase and tutorials, and there also will be an adjoint school, the following week (see webpage).

Important dates

Submission of contributed papers: 3 May
Acceptance/Rejection notification: 7 June

Submissions

Prospective speakers are invited to submit one (or more) of the following:

• Original contributions of high quality work consisting of a 5-12 page extended abstract that provides sufficient evidence of results of genuine interest and 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.

• Extended abstracts describing high quality work submitted/published elsewhere will also be considered, provided the work is recent and relevant to the conference. These consist of a maximum 3 page description and should include a link to a separate published paper or preprint.

The conference proceedings will be published in a dedicated Proceedings issue of the new Compositionality journal:

http://www.compositionality-journal.org

Only original contributions are eligible to be published in the proceedings.

Submissions should be prepared using LaTeX, and must be submitted in PDF format. Use of the Compositionality style is encouraged. Submission is done via EasyChair:

https://easychair.org/conferences/?conf=act2019

Program chairs

John Baez (U.C. Riverside)
Bob Coecke (University of Oxford)

Program committee

Bob Coecke (chair)
John Baez (chair)
Christina Vasilakopoulou
David Moore
Josh Tan
Stefano Gogioso
Brendan Fong
Steve Lack
Simona Paoli
Joachim Kock
Kathryn Hess Bellwald
Tobias Fritz
David I. Spivak
Ross Duncan
Dan Ghica
Valeria de Paiva
Jeremy Gibbons
Samuel Mimram
Aleks Kissinger
Jamie Vicary
Martha Lewis
Nick Gurski
Dusko Pavlovic
Chris Heunen
Corina Cirstea
Helle Hvid Hansen
Dan Marsden
Simon Willerton
Pawel Sobocinski
Dominic Horsman
Nina Otter
Miriam Backens

Steering committee

John Baez (U.C. Riverside)
Bob Coecke (University of Oxford)
David Spivak (M.I.T.)
Christina Vasilakopoulou (U.C. Riverside)


Symposium on Compositional Structures 3

28 January, 2019

One of the most lively series of conferences on applied category theory is ‘SYCO’: the Symposium on Compositional Structures. And the next one is coming soon!

Symposium on Compositional Structures 3, University of Oxford, 27-28 March, 2019.

The Symposium on Compositional Structures (SYCO) is an interdisciplinary series of meetings aiming to support the growing community of researchers interested in the phenomenon of compositionality, from both applied and abstract perspectives, and in particular where category theory serves as a unifying common language. The first SYCO was in September 2018 at the University of Birmingham. The second SYCO was in December 2019, at the University of Strathclyde, each attracting about 70 people.

We welcome submissions from researchers across computer science, mathematics, physics, philosophy, and beyond, with the aim of fostering friendly discussion, disseminating new ideas, and spreading knowledge between fields. Submission is encouraged for both mature research and work in progress, and by both established academics and junior researchers, including students.

Submission is easy, with no format requirements or page restrictions. The meeting does not have proceedings, so work can be submitted even if it has been submitted or published elsewhere. Think creatively—you could submit a recent paper, or notes on work in progress, or even a recent Masters or PhD thesis.

While no list of topics could be exhaustive, SYCO welcomes submissions with a compositional focus related to any of the following areas, in particular from the perspective of category theory:

• logical methods in computer science, including classical and quantum programming, type theory, concurrency, natural language processing and machine learning;

• graphical calculi, including string diagrams, Petri nets and
reaction networks;

• languages and frameworks, including process algebras, proof nets, type theory and game semantics;

• abstract algebra and pure category theory, including monoidal
category theory, higher category theory, operads, polygraphs, and
relationships to homotopy theory;

• quantum algebra, including quantum computation and representation theory;

• tools and techniques, including rewriting, formal proofs and proof assistants, and game theory;

• industrial applications, including case studies and real-world
problem descriptions.

This new series aims to bring together the communities behind many previous successful events which have taken place over the last decade, including “Categories, Logic and Physics”, “Categories, Logicand Physics (Scotland)”, “Higher-Dimensional Rewriting and Applications”, “String Diagrams in Computation, Logic and Physics”, “Applied Category Theory”, the “Simons Workshop on Compositionality”, and the “Peripatetic Seminar in Sheaves and Logic”.

SYCO will be a regular fixture in the academic calendar, running
regularly throughout the year, and becoming over time a recognized venue for presentation and discussion of results in an informal and friendly atmosphere. To help create this community, and to avoid the need to make difficult choices between strong submissions, in the event that more good-quality submissions are received than can be accommodated in the timetable, the programme committee may choose to defer some submissions to a future meeting, rather than reject them. This would be done based largely on submission order, giving an incentive for early submission, but would also take into account other requirements, such as ensuring a broad scientific programme. Deferred submissions can be re-submitted to any future SYCO meeting, where they would not need peer review, and where they would be prioritised for inclusion in the programme. This will allow us to ensure that speakers have enough time to present their ideas, without creating an unnecessarily competitive reviewing process. Meetings will be held sufficiently frequently to avoid a backlog of deferred papers.

Invited speakers

• Marie Kerjean, INRIA Bretagne Atlantique

• Alessandra Palmigiano, Delft University of Technology and University of Johannesburg

Important dates

All times are anywhere-on-earth.

• Submission deadline: Friday 15 February 2019
• Author notification: Wednesday 27 February 2019
• Registration deadline: Wednesday 20 March 2019
• Symposium dates: Wednesday 27 and Thursday 28 March 2019

Submissions

Submission is by EasyChair, via the following link:

https://easychair.org/conferences/?conf=syco3

Submissions should present research results in sufficient detail to allow them to be properly considered by members of the programme committee, who will assess papers with regards to significance, clarity, correctness, and scope. We encourage the submission of work in progress, as well as mature results. There are no proceedings, so work can be submitted even if it has been previously published, or has been submitted for consideration elsewhere. There is no specific formatting requirement, and no page limit, although for long submissions authors should understand that reviewers may not be able to read the entire document in detail.

Financial support

Some funding is available to cover travel and subsistence costs, with a priority for PhD students and junior researchers. To apply for this funding, please contact the local organizers Antonin Delpeuch (antonin.delpeuch@cs.ox.ac.uk) or Ben Musto (benjamin.musto@cs.ox.ac.uk) with subject line “SYCO 3 funding request” by March 6, with a short statement of your current status, travel costs and funding required.

Programme committee

Fatimah Ahmadi, University of Oxford
Corina Cirstea, University of Southampton
Bob Coecke, University of Oxford
Carmen Maria Constantin, University of Oxford
Antonin Delpeuch, University of Oxford
Brendan Fong, Massachusetts Institute of Technology
Dan Ghica, University of Birmingham
Giuseppe Greco, Utrecht University
Helle Hvid Hansen, Delft University
Jules Hedges, University of Oxford
Chris Heunen, University of Edinburgh
Dominic Horsman, University of Grenoble
Dimitri Kartsaklis, Apple
Aleks Kissinger, Radboud University Nijmegen
Alexander Kurz, Chapman University
Jean-Simon Lemay, University of Oxford
Martha Lewis, University of Amsterdam
Dan Marsden, University of Oxford
Samuel Mimram, École Polytechnique
Nina Otter, UCLA
Simona Paoli, University of Leicester
Robin Piedeleu, University of Oxford
David Reutter, University of Oxford
Christine Tasson, Paris Diderot University
Jamie Vicary, University of Birmingham
Tamara von Glehn, University of Cambridge
Quanlong Wang, University of Oxford
Gijs Wijnholds, Queen Mary University of London
Philipp Zahn, University of St.Gallen


Applied Category Theory 2019 — Adjoint School

5 January, 2019

Dear scientists, mathematicians, linguists, philosophers, and hackers:

We are writing to let you know about a fantastic opportunity to learn about the emerging interdisciplinary field of applied category theory from some of its leading researchers at the ACT2019 Adjoint School. It will begin February 18, 2019 and culminate in a meeting in Oxford, July 22–26, right after the associated conference. Applications are due January 30th; see below for details.

Applied category theory is a topic of interest for a growing community of researchers, interested in studying systems of all sorts using category-theoretic tools. These systems are found in the natural sciences and social sciences, as well as in computer science, linguistics, and engineering. The background and experience of our community’s members is as varied as the systems being studied.

The goal of the ACT2019 School is to help grow this community by pairing ambitious young researchers together with established researchers in order to work on questions, problems, and conjectures in applied category theory.

Who should apply

Anyone from anywhere 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, and post-docs. We ask that you commit to the full program as laid out below.

Instructions for how to apply can be found below the research topic descriptions.

Senior research mentors and their topics

Below is a list of the senior researchers, each of whom describes a research project that their team will pursue, as well as the background reading that will be studied between now and July 2019.

Miriam Backens

Title: Simplifying quantum circuits using the ZX-calculus

Description: The ZX-calculus is a graphical calculus based on the category-theoretical formulation of quantum mechanics. A complete set of graphical rewrite rules is known for the ZX-calculus, but not for quantum circuits over any universal gate set. In this project, we aim to develop new strategies for using the ZX-calculus to simplify quantum circuits.

Background reading:

  1. Matthes Amy, Jianxin Chen, Neil Ross. A finite presentation of CNOT-Dihedral operators.
  2. Miriam Backens. The ZX-calculus is complete for stabiliser quantum mechanics.

Tobias Fritz

Title: Partial evaluations, the bar construction, and second-order stochastic dominance

Description: We all know that 2+2+1+1 evaluates to 6. A less familiar notion is that it can partially evaluate to 5+1. In this project, we aim to study the compositional structure of partial evaluation in terms of monads and the bar construction and see what this has to do with financial risk via second-order stochastic dominance.

Background reading:

  1. Tobias Fritz and Paolo Perrone. Monads, partial evaluations, and rewriting.
  2. Maria Manuel Clementino, Dirk Hofmann, George Janelidze. The monads of classical algebra are seldom weakly cartesian.
  3. Todd Trimble. On the bar construction.

Pieter Hofstra

Title: Complexity classes, computation, and Turing categories

Description: Turing categories form a categorical setting for studying computability without bias towards any particular model of computation. It is not currently clear, however, that Turing categories are useful to study practical aspects of computation such as complexity. This project revolves around the systematic study of step-based computation in the form of stack-machines, the resulting Turing categories, and complexity classes. This will involve a study of the interplay between traced monoidal structure and computation. We will explore the idea of stack machines qua programming languages, investigate the expressive power, and tie this to complexity theory. We will also consider questions such as the following: can we characterize Turing categories arising from stack machines? Is there an initial such category? How does this structure relate to other categorical structures associated with computability?

Background reading:

  1. J.R.B. Cockett and P.J.W. Hofstra. Introduction to Turing categories. APAL, Vol 156, pp. 183-209, 2008.
  2. J.R.B. Cockett, P.J.W. Hofstra and P. Hrubes. Total maps of Turing categories. ENTCS (Proc. of MFPS XXX), pp. 129-146, 2014.
  3. A. Joyal, R. Street and D. Verity. Traced monoidal categories. Mat. Proc. Cam. Phil. Soc. 3, pp. 447-468, 1996.

Bartosz Milewski

Title: Traversal optics and profunctors

Description: In functional programming, optics are ways to zoom into a specific part of a given data type and mutate it. Optics come in many flavors such as lenses and prisms and there is a well-studied categorical viewpoint, known as profunctor optics. Of all the optic types, only the traversal has resisted a derivation from first principles into a profunctor description. This project aims to do just this.

Background reading:

  1. Bartosz Milewski. Profunctor optics, categorical view.
  2. Craig Pastro, Ross Street. Doubles for monoidal categories.

Mehrnoosh Sadrzadeh

Title: Formal and experimental methods to reason about dialogue and discourse using categorical models of vector spaces

Description: Distributional semantics argues that meanings of words can be represented by the frequency of their co-occurrences in context. A model extending distributional semantics from words to sentences has a categorical interpretation via Lambek’s syntactic calculus or pregroups. In this project, we intend to further extend this model to reason about dialogue and discourse utterances where people interrupt each other, there are references that need to be resolved, disfluencies, pauses, and corrections. Additionally, we would like to design experiments and run toy models to verify predictions of the developed models.

Background reading:

  1. Gerhard Jager (1998): A multi-modal analysis of anaphora and ellipsis. University of Pennsylvania Working Papers in Linguistics 5(2), p. 2.
  2. Matthew Purver, Ronnie Cann, and Ruth Kempson. Grammars as parsers: meeting the dialogue challenge. Research on Language and Computation, 4(2-3):289–326, 2006.

David Spivak

Title: Toward a mathematical foundation for autopoiesis

Description: An autopoietic organization—anything from a living animal to a political party to a football team—is a system that is responsible for adapting and changing itself, so as to persist as events unfold. We want to develop mathematical abstractions that are suitable to found a scientific study of autopoietic organizations. To do this, we’ll begin by using behavioral mereology and graphical logic to frame a discussion of autopoeisis, most of all what it is and how it can be best conceived. We do not expect to complete this ambitious objective; we hope only to make progress toward it.

Background reading:

  1. Brendan Fong, David Jaz Myers, David Spivak. Behavioral mereology.
  2. Brendan Fong, David Spivak. Graphical regular logic.
  3. Luhmann. Organization and Decision, CUP. (Preface)

School structure

All of the participants will be divided up into groups corresponding to the projects. A group will consist of several students, a senior researcher, and a TA. Between January and June, we will have a reading course devoted to building the background necessary to meaningfully participate in the projects. Specifically, two weeks are devoted to each paper from the reading list. During this two week period, everybody will read the paper and contribute to discussion in a private online chat forum. There will be a TA serving as a domain expert and moderating this discussion. In the middle of the two week period, the group corresponding to the paper will give a presentation via video conference. At the end of the two week period, this group will compose a blog entry on this background reading that will be posted to the n-category cafe.

After all of the papers have been presented, there will be a two-week visit to Oxford University, 15–26 July 2019. The second week is solely for participants of the ACT2019 School. Groups will work together on research projects, led by the senior researchers.

The first week of this visit is the ACT2019 Conference, where the wider applied category theory community will arrive to share new ideas and results. It is not part of the school, but there is a great deal of overlap and participation is very much encouraged. The school should prepare students to be able to follow the conference presentations to a reasonable degree.

To apply

To apply please send the following to act2019school@gmail.com by January 30th, 2019:

  • Your CV
  • A document with:
    • An explanation of any relevant background you have in category theory or any of the specific projects areas
    • The date you completed or expect to complete your Ph.D and a one-sentence summary of its subject matter.
  • Order of project preference
  • To what extent can you commit to coming to Oxford (availability of funding is uncertain at this time)
  • A brief statement (~300 words) on why you are interested in the ACT2019 School. Some prompts:
    • how can this school contribute to your research goals?
    • how can this school help in your career?

Also have sent on your behalf to act2019school@gmail.com a brief letter of recommendation confirming any of the following:

  • your background
  • ACT2019 School’s relevance to your research/career
  • your research experience

Questions?

For more information, contact either
– Daniel Cicala. cicala (at) math (dot) ucr (dot) edu
– Jules Hedges. julian (dot) hedges (at) cs (dot) ox (dot) ac (dot) uk