Research School on Bicategories, Categorification and Quantum Theory

University of Leeds, UK
11-16 July 2022

Introduction

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.

Courses

The school will feature four 4-hour courses given by expert researchers from across the globe.

Bicategories

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.

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Monoidal Categories Like That of 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.

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Categorification

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.

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Hopf Algebras

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.

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Research Lecture

The conference will also feature a special research lecture.

Important Dates

  • Pre-Registration Deadline: Friday 29 April 2022
  • Notification of Acceptance: Friday 6 May 2022 Friday 13 May 2022
  • Summer School: 11-16 July 2022

Fees and Financial Support

Registration costs will be as follows. These costs include accommodation, breakfast, lunch, and coffee breaks.

  • 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

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 Information

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:

Programme

The programme of lectures will be announced closer to the time. A typical day will involve three 1-hour lectures and a tutorial session.

Organizers

If you have a question about the Research School, please get in touch with one of the organizers.