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Categorification in Representation Theory (MIEMIETZVU20SCIEP)


Project Description

In the last 20 years, major progress in representation theory, low-dimensional topology and related areas has been made through the process of categorification. This refers to the process of considering higher categorical objects with extra layers of information, whose decategorified shadows (when forgetting the extra information) describe the original problem one is interested in solving.

In practice, this usually means that instead of considering a group or an algebra acting on a vector space by linear transformations, one studies a so-called 2-category (a gadget with objects, 1-morphisms and 2-morphisms – the 1-morphisms categorifying the elements in the group or algebra) acting on categories by functors.

In specific examples (e.g. 2-categories categorifying Lie algebra or Hecke algebras), major breakthroughs in long open problems have been achieved in this way, such as the computation of decomposition numbers for Hecke algebras, a proof of the Kazhdan-Lusztig conjectures for all Coxeter groups, and counterexamples to James’ conjecture. Inspired by this, there has been an ongoing effort to develop an abstract 2-representation theory that captures the successful examples and provides a framework for future ones.

In this project, the student will work on both questions from abstract 2-representation theory, and on applying those to examples relevant in classical representation theory.

For more information on the supervisor for this project, please go here: https://people.uea.ac.uk/v_miemietz

This is a PhD programme.

The start date of the project is 1 October 2020.

The mode of study is full-time. The studentship length is 3.5 years.

Entry requirements:

Acceptable first degree in Mathematics.

The standard minimum entry requirement is 2:1.

Funding Notes

This PhD project is in an EPSRC studentship competition within the Faculty of Science. Funding is for 3.5 years and will be available to successful candidates who meets the UK Research Council eligibility criteria. These requirements are detailed in the Research Council Training Grant Guide which can be found at View Website (see Annex 1 for Residential Guidelines for Research Council Studentships). In most cases UK and EU nationals who have been ordinarily resident in the UK for 3 years prior to the start of the course are eligible for a full-award. Other EU nationals may qualify for a fees-only award.

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