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Higher representation theory and categorification (MIEMIETZVU20SF)

  • Full or part time
  • Application Deadline
    Sunday, May 31, 2020
  • Self-Funded PhD Students Only
    Self-Funded PhD Students Only

Project Description

This PhD project will investigate questions surrounding categorification in representation theory.
Categorification has led to many breakthroughs in representation theory in the last 15 years. It is roughly speaking, a (non-constructive) process by which algebras acting on vector spaces are replaced by 2-categories acting on categories. This gives rise to new methods to tackle long-standing problems and has led for example led to a proof of Broué’s conjecture for symmetric groups, and algebraic proof of the Kazhdan-Lusztig conjecture for all Coxeter groups, and the computation of decomposition numbers for Hecke algebras.

The PhD project will focus on both advancing the general theory and studying special classes of examples of categorification, e.g. coming from Soergel bimodules, which categorify Hecke algebras. The technical ingredients for the project will come from classical representation theory, category theory and homological algebra.


MORE INFORMATION

Project supervisor: https://people.uea.ac.uk/v_miemietz
Mode of study: Full time
Start date: October 2020
Entry requirements: First degree (2:1 or above) in Mathematics.

Funding Notes

This PhD project is offered on a self-funding basis. It is open to applicants with funding or those applying to funding sources. Details of tuition fees can be found at View Website.

A bench fee is also payable on top of the tuition fee to cover specialist equipment or laboratory costs required for the research. The amount charged annually will vary considerably depending on the nature of the project and applicants should contact the primary supervisor for further information about the fee associated with the project.

References

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

ii) V.Mazorchuk, Classification problems in 2-representation theory. São Paulo J. Math. Sci. 11 (2017), no. 1, 1–22

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

Related Subjects

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