Coventry University Featured PhD Programmes
University of Southampton Featured PhD Programmes
University College London Featured PhD Programmes

Higher representation theory and categorification (MIEMIETZVU20SF)


School of Mathematics

This project is no longer listed on FindAPhD.com and may not be available.

Click here to search FindAPhD.com for PhD studentship opportunities
Dr V Miemietz No more applications being accepted Self-Funded PhD Students Only

About the Project

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 http://www.uea.ac.uk/study/postgraduate/research-degrees/fees-and-funding.

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
Search Suggestions

Search Suggestions

Based on your current searches we recommend the following search filters.



FindAPhD. Copyright 2005-2021
All rights reserved.