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Details of Grant 

EPSRC Reference: EP/S017216/1
Title: 2-representation theory and categorification
Principal Investigator: Miemietz, Dr V
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Mathematics
Organisation: University of East Anglia
Scheme: Standard Research
Starts: 01 April 2019 Ends: 31 March 2022 Value (£): 329,519
EPSRC Research Topic Classifications:
Algebra & Geometry
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
05 Sep 2018 EPSRC Mathematical Sciences Prioritisation Panel September 2018 Announced
Summary on Grant Application Form
While in mathematics it is very often helpful to break complicated problems down into less complicated ones by simplifying and forgetting data, the converse has often proved useful. The term categorification refers to the process of finding more complicated structures which, upon forgetting some information, reproduce the original problem that one wants to study. The more complicated structures often allow us to deduce useful information that was previously inaccessible. For example, an integer number solving a certain equation might a priori be anything, but if we then discover that this certain number, in fact, describes the number of elements in a set (e.g. cats in a household), it cannot be negative.

Categorification in representation theory is usually formulated in terms of certain structures called 2-categories encoding generalised symmetries of other categories, or in other words, 2-representations of 2-categories. To develop the theory of 2-representations of 2-categories (with certain nice properties abstracted from interesting examples) and to apply them to some of the original problems that inspired their definition is the aim of this proposal.
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