This Research School features four introductory courses on modern categorical algebra and its application to quantum theory. The goal is to provide a forum for graduate students and junior researchers to gain a strong technical foundation in this rich and dynamic area, and to meet some of the leading researchers in the area. There will also be many opportunities for networking with other students and researchers.
The school will feature four courses given by expert researchers from across the globe. Tutorial sessions given by expert teaching assistants will help participants learn the material. There will be many opportunities for informal interaction and networking. Prerequisites. To get the most from the courses, participants should already have basic knowledge of category theory (categories, functors, natural transformations, isomorphisms, limits and colimits), and individual courses have further mild prerequisites given below.
Just as monoids have categories as a many-object generalisation, so
monoidal categories have a many-object generalisation, which are
Benabou's bicategories. This course will study bicategories in their
guise as many-object monoidal categories. Particular attention will be paid to the notion of enrichment in a
monoidal category or in a bicategory. Besides examining a range of
standard examples, we will also discuss how to set up bespoke
enrichments using the theory of free presentations of cocomplete
monoidal categories and bicategories.
Prerequisites: Basic category theory.
Teaching Assistant: Christina Vasilakopoulou, University of Patras
Categories like Hilbert Spaces
Hilbert spaces are the mathematical foundation of quantum theory. This course concerns the abstract structure of the monoidal dagger category they form. We identify conceptual ingredients for quantum computation, such as dual objects and Frobenius structures to model entanglement and measurement. Spatiotemporal structure is discussed not only via the graphical calculus, but also in terms of subunits and sheaves.
Prerequisites: Basic ideas about Hilbert spaces (adjoint operator, orthonormal basis, tensor product), basic ideas about point-set and pointless topology (topological space, frame, locales).
Tutorial 1 Answers,
Tutorial 2 Answers,
Tutorial 3 Answers,
Teaching Assistant: Carmen Constantin, University of Edinburgh and Mansfield College, Oxford.
These lectures will motivate and explain finitary bicategories and their finitary birepresentations, their cell theory, the relationship between birepresentations and coalgebra 1-morphisms via the internal hom construction. This will be supported by explicit small examples and culminate in an extended example considering the categorification of Hecke algebras via Soergel bimodules.
Prerequisites: Basic representation theory of finite-dimensional algebras, for example the first few sections of Alex Bartel's notes.
Teaching Assistant: James MacPherson, University of East Anglia
We shall discuss the structure of Hopf algebras, focusing on classification problems in the finite dimensional and, in particular, in the semisimple case. Some of their main features and invariants will be discussed. We shall study the connection with tensor categories through their representation theory and discuss a number of applications and open problems.
Prerequisites: Algebras over fields, modules for algebras.
Teaching Assistant: Aryan Ghobadi, Queen Mary University of London
The conference will also feature a special research lecture.
The beauty of braids
Via different perspectives on braids we indicate how the search for topological invariants leads to crucial developments in representation theory and to speculations on higher topological invariants and TQFTs.
All sessions take place in the Roger Stevens Lecture Theatre 22 at the University of Leeds.
|Time||Monday 11 July||Tuesday 12 July||Wednesday 13 July||Thursday 14 July||Friday 15 July|
|0930-1100||Bicategories 1||Tutorial 1||Hopf 2||Bicategories 3||Tutorial 3|
|1130-1300||Categorification 1||Bicategories 2||Tutorial 2||Categorification 3||Research Lecture|
|1400-1530||Hopf 1||Categorification 2||Hopf 3|
|1600-1730||Quantum 1||Quantum 2||Quantum 3|
|Robert Allen, University of Bristol||Agoston Kaposi, Eötvös Loránd University||
Rhiannon Savage, The University of Oxford
|Sarah Almateari, University of Leeds||Keisuke Hoshino, RIMS, Kyoto University||
Nino Scalbi, Instituto Superior Técnico
|Brad Ashley, The University Of Sheffield||Matthew Koban, University of Toronto||Léo Schelstraete, UCLouvain|
|Nicolas Blanco, University of Birmingham||Zoltán Kolarovszki, Eötvös Loránd University||
Arber Selimi, Instituto Superior Técnico, Lisbon
|Dylan Braithwaite , University of Strathclyde||Fernando Liu Lopez, Rice University||
Andrew Slattery, University of Leeds
|Elena Caviglia, University of Leicester||Gabriele Lobbia, Masaryk University||
Matteo Spadetto, University of Leeds
|Cole Comfort, University of Oxford||Leo Lobski, University College London||
Benjamin Spencer, Indiana University
|Carmen Constantin, University of Edinburgh||Martino Lupini, Newcaste University||
Miloslav Štepán, Masaryk University
|Alexander Corner, Sheffield Hallam University||Marco Mackaaij, University of Algarve||
Mateusz Stroinski, Uppsala University
|Alexander Cowtan, University of Oxford||James Macpherson, University of East Anglia||
Catherina Stroppel, University of Bonn
|Jonathan Davies, University of Nottingham||Ioannis Markakis, University of Cambridge||
Filippos Ilarion Sytilidis, Oxford University
|Will Donovan, Yau MSC, Tsinghua U||Maciej Markiewicz, University of Warsaw||
Calin Tataru, University of Cambridge
|Ali Elokl, North Carolina State University||Joseph Martin, University of Sheffield||
Mrudul Thatte, Columbia University
|Diogo Freire de Andrade, Instituto Superior Técnico||Emily McGovern, North Carolina State University||
Vincent Thompson, Rice University
|Zeinab Galal, University of Leeds||Luca Mesiti, University of Leeds||
Fiona Torzewska, University of Leeds
|Nicola Gambino, University of Leeds||Vanessa Miemietz, University of East Anglia||Sachin Valera, NYUAD|
|Richard Garner, Macquarie University||Antonio Michele Miti, MPI Bonn||
Bram Vancraeynest-De Cuiper, Ghent University
|Aryan Ghobadi, Queen Mary||Charles Nsukukazifani Msipha, Tshwane University of Technology||
Christina Vasilakopoulou, University of Patras
|Mahdie Hamdan, Cardiff University||Sonia Natale, Universidad Nacional de Córdoba||
Pedro Vaz, Université catholique de Louvain
|Samuel Hannah, Cardiff University||Federico Olimpieri, University of Leeds||
Florrie Verity, Australian National University
|Marius Henry, University of Cambridge||Isaac Packtor, DePaul University||
Jamie Vicary, University of Cambridge
|Chris Heunen, University of Edinburgh||Aberdeen Powell, University of East Anglia||
Elia Vincenzi, Università di Roma Tor Vergata
|Kengo Hirata, RIMS, Kyoto University||Jan Pulmann, University of Edinburgh||
Abigail Watkins, Indiana University
|Nick Hu, University of Oxford||Manar Qadi, University of Leeds||
Haiqi Wu, ETH Zürich / University of Cambridge
|Edward Jones-Healey, University of Manchester||Jack Romo, University of Leeds||
Tony Zorman, Technische Universität Dresden
|Helena Jonsson, Uppsala university||
Chiara Sarti, University of Cambridge
Accommodation during the Research School will be provided at Storm Jameson Court, a new high-standard accommodation block with a lounge area and a 24-hour reception service. The cost of accommodation is covered by the registration fee.
During the Research School, the lectures will be in the Roger Stevens Building, and coffee breaks will be in the School of Mathematics.
Further information on travel to Leeds and the campus itself is available here:
Pre-Registration Deadline: Friday 29 April 2022 Notification of Acceptance: Friday 6 May 2022Friday 13 May 2022
- Summer School: 11-15 July 2022
Fees and Financial Support
Registration is now closed.
Registration costs will be as follows. These costs include accommodation, breakfast, lunch, coffee breaks, and the conference dinner which will take place one evening during the school.
- PhD students: £150
- Early-Career Researchers (up to 5 years since PhD): £250
- Senior Researchers: £500
To apply for a place you must pre-register. Some financial support is also available, which may reduce the cost below that stated above. A financial support request can be filled out as part of the pre-registration.
Pre-registration is now closed.
Pre-registration allows you to express your interest in attending. Due to space restrictions in the venue, we may not be able to accept all applications. The deadline for pre-registration is April 29. Pre-registration is available using the following online form:
Local Organising Committee
Nicola Gambino, Luca Mesiti, Federico Olimpieri, Andrew Slattery, Matteo Spadetto, Florrie Verity and Zeinab Galal.
The lunch at the conference is provided by the university refectory. They can advise on the following allergens as ingredients in each food item: celery, gluten, crustaceans, eggs, fish, lupin, milk, molluscs, mustard, nuts, peanuts, sesame seeds, soya and sulphur dioxide. However, it is a conventional kitchen where all food and drinks are prepared in the same space, and so they cannot guarantee that any dish will not contain traces of any allergen.