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2-representation theory and applications in categorification (MIEMIETZVU19 SCIC2)

  • Full or part time
  • Application Deadline
    Thursday, April 04, 2019
  • Competition Funded PhD Project (Students Worldwide)
    Competition Funded PhD Project (Students Worldwide)

Project Description

In recent years, major breakthroughs in representation theory have been achieved through categorification, in which, roughly speaking, vector spaces are being replaced by categories, and elements of an algebra acting on a vector space are replaced by functors. The subject studying such categorifications abstractly is called 2-representation theory. This project will study abstract questions in 2-representation theory, as well as their applications to some of the most important examples of categorifications, such as Hecke 2-categories (also known as Soergel bimodules) and Kac-Moody 2-categories (also known as KLR 2-categories). If you are interested in this project, please feel free to contact me informally by email.

For more information on the supervisor for this project, please visit:

Type of programme: PhD

Project start date: October 2019

Mode of study: Full time

Entry requirements: Acceptable first degree - Mathematics. The standard minimum entry requirement is 2:1.

Funding Notes

This PhD project is in a Faculty of Science competition for funded studentships. These studentships are funded for 3 years and comprise UK/EU fees, an annual stipend of £15,009 and £1,000 per annum to support research training. Overseas applicants may apply but they are required to fund the difference between home/EU and overseas tuition fees (which are detailed on the University’s fees pages at View Website . Please note tuition fees are subject to an annual increase).


i) V. Mazorchuk. Lectures on algebraic categorification. QGM Master Class Series. European Mathematical Society (EMS), Zürich, 2012.

ii) V. Mazorchuk, V. Miemietz. Transitive 2-representations of finitary 2-categories. Trans. Amer. Math. Soc. 368, 2016, no. 11, 7623-7644.

iii) B. Elias, G. Williamson. The Hodge theory of Soergel bimodules, Ann. of Math. (2) 180 (2014), no.3 , 1089-1136.

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