20/10/2020
The Human Resources Strategy for Researchers

Categorification in representation theory (MIEMIETZV_U21SF)

This job offer has expired


  • ORGANISATION/COMPANY
    University of East Anglia
  • RESEARCH FIELD
    Biological sciencesOther
    Computer scienceOther
    MathematicsOther
  • RESEARCHER PROFILE
    First Stage Researcher (R1)
  • APPLICATION DEADLINE
    31/05/2021 23:00 - Europe/London
  • LOCATION
    United Kingdom › Norwich
  • TYPE OF CONTRACT
    Other
  • JOB STATUS
    Other
  • OFFER STARTING DATE
    01/10/2021

OFFER 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. On the most basic level (going in some sense from categorical level zero to level 1), vector spaces over a fixed field categorify natural numbers. By taking the dimension of a vector space, we can reproduce a natural number, but we have additional information for vector spaces when looking at linear maps from one to the other that are not visible purely on the level of dimensions. In representation theory, one typically looks at passing from categorical level one to categorical level 2, and roughly speaking, replaces algebras acting on vector spaces (in classical representation theory) by higher categorical objects, more specifically 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 abelian defect group conjecture for symmetric groups, an algebraic proof of the Kazhdan--Lusztig conjectures for all Coxeter types, and counterexamples to James’ conjecture.

 

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 of finite-dimensional algebras, category theory and homological algebra.

Length of Studentship:  3 year studentships have a (non-funded) 1 year ‘registration only’ period

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 https://www.uea.ac.uk/about/university-information/finance-and-procurement/finance-information-for-students/tuition-fees

 

A bench fee is also payable on top of the tuition fee to cover specialist equipment or laboratory costs required for the research. Applicants should contact the primary supervisor for further information about the fee associated with the project.

More Information

Offer Requirements

Specific Requirements

Acceptable first degree is Mathematics

The standard minimum entry requirement is 2:1

Work location(s)
1 position(s) available at
University of East Anglia
United Kingdom
Norwich
NR4 7TJ

EURAXESS offer ID: 569475

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