Meetings

To claim travel expenses:

1.  Download this form, fill in parts A,B,C,D, and in part C  write 'CATNIP meeting' with the date of the meeting.

2. Collate all your travel receipts in a single pdf file with your name, and also rename the claim form with your name. 

3. Send these two documents to simona.paoli@abdn.ac.uk  by Monday 15 May  2024. 

The meeting is open to everybody. Participants from the three nodes may be offered travel reimbursement. We hope to be able to reimburse all staff and PhD students from the nodes, but if (depending on participants numbers) any budget issues arise priority will be given to PhD students and early career researchers. Please register here.

Location: The talks will be in the McCance building in room MC301. 

Programme

10.30-11.00: Welcome with tea
11.00-12.00: Dan Marsden (University of Nottingham): "The Graphical Theory of Monads"
12.00-13.30: Lunch
13.30-14.30: Rita Fatimah Ahmadi (Imperial College London): "Bicategory of Topological Quantum Computation"
14.30-15.30: Neil Ghani (University of Strathclyde): "A Fibrational Approach to Differentiation"
15.30-16.00: Coffee Break
16.00-17.00: John Baez (University of California, Riverside): "Software for Compositional Modeling"

Participants:

• Jules Hedges (University of Strathclyde)

• John Baez (University of California, Riverside)

• Rita Fatimah Ahmadi (Imperial College London)

• Neil Ghani (University of Strathclyde)

• Dan Marsden (University of Nottingham)

• Simona Paoli (University of Aberdeen)

• Chris Heunen (University of Edinburgh)

• Fredrik Nordvall Forsberg (University of Strathclyde)

• Adrián Doña Mateo (University of Edinburgh)

• Malthe Sporring (University of Edinburgh)

• Arthur Harman (University of Edinburgh)

• Malin Altenmüller (University of Strathclyde)

• Nesta van der Schaaf (University of Edinburgh)

• Swaraj Dash (Heriot-Watt University)

• Kengo Hirata (University of Edinburgh)

• Matthew Di Meglio (University of Edinburgh)

• Lucy Spouncer (University of Edinburgh)

• Adithya Sireesh (University of Edinburgh)

• Robert Booth (University of Edinburgh)

• Ioannis Markakis (University of Cambridge)

• Wilf Offord (University of Cambridge)

• Thibaut Benjamin (University of Cambridge)

• Radu Mardare (University of Strathclyde)

• Dilsat Bilal Yuksel (University of Strathclyde)

• Riu Rodriguez Sakamoto (University of Strathclyde)

• Dylan Braithwaite (University of Strathclyde)

• Clemens Kupke (University of Strathclyde)

• Ezra Schoen (University of Strathclyde)

• Andre Videla (University of Strathclyde)

Titles and Abstracts:

John Baez: "Software for Compositional Modeling"

Mathematical models of human interactions are important and widely used in epidemiology, but building and working with these models at scale is challenging.  I will explain two software tools for doing this, both based on category theory.   Modelers often regard diagrams as an informal step toward a mathematically rigorous formulation of a model.   Giving these diagrams a precise syntax using category theory has many advantages, but I will focus on those connected to "community based modeling": the process of working with diverse community members to build a model.   The next step is to tackle "agent-based models" and use them to help plan our response to climate change.

References:

• John Baez, Xiaoyan Li, Sophie Libkind, Nathaniel Osgood and Evan Patterson, Compositional modeling with stock and flow diagrams, Proceedings Fifth International Conference on Applied Category Theory, EPTCS 380 (2022), 77-96. 

• John Baez, Xiaoyan Li, Sophie Libkind, Nathaniel D. Osgood and Eric Redekopp, A categorical framework for modeling with stock and flow diagrams, to appear in Mathematics for Public Health, Springer.

Rita Fatimah Ahmadi: "Bicategory of Topological Quantum Computation"

Unitary Ribbon Fusion Categories (URFC) formalise anyonic theories. It has been widely assumed the same category formalises a model of topological quantum computation. However, we recently addressed and resolved this confusion and demonstrated while the former could be any fusion category, the latter is always a subcategory of \textbf{Hilb}. In this talk, I argue a categorical formalism which captures and unifies both an anyonic theory and corresponding models of topological quantum computation is a braided (fusion) bicategory.

References:

• A short survey on topological quantum computation: https://arxiv.org/pdf/1601.05288.pdf

• A longer version (If interested): https://arxiv.org/pdf/1705.06206.pdf

• The difference between the category for an anyonic theory and topological quantum computing category: https://arxiv.org/abs/2211.03855

• Blogposts/TQC.md at master · RitaAhmadi/Blogposts · GitHub 

Neil Ghani: "A fibrational approach to differentiation"

With the growth of machine learning, there has been a renewed focus on differential geometry. In this talk I'll describe recent work on a fibrational unification of different differentiation doctrines.

References

• Robin Cockett, Geoffrey Cruttwell, Jonathan Gallagher, Jean-Simon Pacaud Lemay, Benjamin MacAdam, Gordon Plotkin, Dorette Pronk – Reverse Derivative Categories

• Cockett & Cruttwell – Differential tangent structure, and SDG

Dan Marsden: "The Graphical Theory of Monads"

The formal theory of monads shows that much of the theory of monads can be developed in the abstract at the level of 2-categories. This means that results about monads can established once and for all, and simply instantiated in settings such as enriched category theory.

Unfortunately, these results can be hard to reason about as they involve more abstract machinery. In this talk, I shall present the formal theory of monads in terms of string diagrams --- a graphical language for categorical calculations. Using this perspective, I will show that many aspects of the theory of monads, such as the Eilenberg-Moore and Kleisli resolutions of monads, liftings, and distributive laws can be understood in terms of systematic graphical calculational reasoning.

The talk will serve as an introduction both to the formal theory of monads and to the use of string diagrams in non-trivial calculations, in particular, their application to calculations in monad theory. (Joint work with Ralf Hinze).

References

• Ralf Hinze & Dan Marsden - Equational reasoning with lollipops, forks, cups, caps, snakes, and speedometers

• Ralf Hinze & Dan Marsden - Dragging Proofs Out of Pictures

The meeting is open to everybody. Participants from the three nodes may be offered travel reimbursement. We hope to be able to reimburse all staff and PhD students from the nodes, but if (depending on participants numbers) any budget issues arise priority will be given to PhD students and early career researchers. Please register here.

Programme

11.00-11.30: Welcome with tea
11.30-12.30: Vanessa Miemietz (University of East Anglia): "Categorification in Representation Theory"
12.30-13.30: Lunch
13.30-14.30: Elena di Lavore (Tallinn University of Technology): "Partial Markov Categories"
14.30-15.00: Panel discussion: "Encouraging women to apply for PhDs"
15.00-15.30: Tea
15.30-16.30: Nicola Gambino (University of Manchester): "Two-dimensional categorical logic"
16.30-17.30: Social drinks

The talks will be available over zoom at https://ed-ac-uk.zoom.us/j/83331873132 (Passcode: Noether99).

Vanessa Miemitz: "Categorification in Representation Theory"

Abstract: I will try to explain and motivate the ideas behind categorification in representation theory, before explaining in more detail some results on the specific example of Soergel bimodules, which categorify Hecke algebras.

Background material:

• Aaron Lauda and Joshua Sussan, An inviation to categorification.

• Volodymyr Mazorchuk, Lectures on algebraic categorification.

• Alistair Savage, Introduction to Categorification.

• John C. Baez and James Dolan, Categorification.

Elena di Lavore: "Partial Markov Categories"

Abstract: I will present partial Markov categories, giving an introduction to Markov categories and cartesian restriction categories. Markov categories encode stochastic processes and cartesian restriction categories encode deterministic processes with constraints. In the same way, partial Markov categories encode stochastic processes with constraints, observations and updates. In particular, we prove a synthetic Bayes theorem. This is recent joint work with Mario Román.

Background material: 

• Tobias Fritz, A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics.

• Robin Cockett and Steve Lack, Restriction categories I: categories of partial maps.

• Ivan Di Liberti, Fosco Loregian, Chad Nester and Paweł Sobociński, Functorial semantics for partial theories.
  A nice introduction with beautiful diagrams can be found in Chad's slides for SYCO 5.

• Elena Di Lavore and Mario Román, Evidential decision theory via partial Markov categories.

Nicola Gambino: "Two-dimensional categorical logic"

Abstract: Categorical logic, founded by Lawvere in the '60s, is generally concerned with the interplay between logic and  category theory, with applications in both directions. In recent years, motivation from various angles, including theoretical computer science, has led to first steps in the creation of two-dimensional categorical logic, in which ordinary set-based structures are replaced by category-based ones (e.g equivalence relations are replaced by groupoids), very much in analogy with the research program of categorification in algebra.

After reviewing the basics of categorical logic and outlining the key aspects of two-dimensional categorical logic, I will focus on an illustrative example, namely the 2-category of analytic functors, introduced in [FGHW] and studied further in [GJ]. This 2-category possesses a wealth of structure, thus giving a good indication of the potential and complexity of two-dimensional categorical logic. In particular, it provides a model of the differential lambda-calculus [ER], an extension of the lambda-calculus with a differential operator, in which it is possible to approximate lambda-terms by a form of the Taylor series expansion [ER2].

Background material:

• [ER] T. Ehrhard and L. Regnier, The differential lambda-calculus.

• [ER2] T. Ehrhard and  L. Regnier, Uniformity and the Taylor expansion of ordinary lambda terms.

• [FGHW] M. Fiore, N. Gambino, M. Hyland and G. Winskel, The cartesian closed bicategory of generalised species of structures.

• [GJ] N. Gambino and A. Joyal, On operads, bimodules and analytic functors.

Participants

• Adithya Sireesh (University of Edinburgh)

• Adrián Doña Mateo (University of Edinburgh )

• Adrian Miranda (University of Manchester)

• Arseniy Kryazhev (UCSD)

• Baylee Schutte (University of Aberdeen)

• Chris Heunen (University of Edinburgh)

• David Dalrymple (Protocol Labs)

• Dylan Braithwaite (University of Strathclyde)

• Eigil Reischel (University of Strathclyde)

• Elena Di Lavore (Tallinn University of Technology)

• Emily Roff (University of Edinburgh)

• Gordon Plotkin (University of Edinburgh)

• Jade Master (University of Strathclyde)

• James Gaunt (Heriot Watt University)

• Jan Pulmann (University of Edinburgh)

• Javier Aguilar Martín (University of Kent)

• Jesse Sigal (University of Edinburgh )

• John Power (Macquarie University)

• Jules Hedges (University of Strathclyde)

• Mario Román (Tallinn University of Technology)

• Mathieu Huot (University of Oxford)

• Matthew Di Meglio (University of Edinburgh)

• Mike Cruchten (University of Sheffield)

• Nesta van der Schaaf (University of Edinburgh)

• Ohad Kammar (University of Edinburgh)

• Parth Shimpi (University of Glasgow )

• Peter Guthmann (University of Aberdeen)

• Richard Hepworth (University of Aberdeen)

• Robert Booth (University of Edinburgh)

• Sergio (ICMAT-UAM)

• Simona Paoli (University of Aberdeen)

• Swaraj Dash (Heriot-Watt University)

• Tom Leinster (University of Edinburgh)

• Vikraman Choudhury (University of Glasgow)

Location

The meeting will take place in the Bayes Centre, in room G.03 on the ground floor.