Computation of matrix factorizations for discriminants of pseudo-reflection groups

Lead Research Organisation: University of Leeds
Department Name: Pure Mathematics


EPSRC : Simon May : EP/R513258/1

This Globalink Research Placement should take place at Carleton University in the Autumn of 2020. It will allow the applicant Simon May to spend 12 weeks at the host university and complement the theoretical work in his Ph.D. thesis with explicit computations of matrix factorizations for discriminants of pseudo-reflection groups. It will also allow the applicant to take part in courses and research seminars at the host University in order to establish collaborations with the host supervisor and his group as well as to grow his professional network.

The background for this work is the McKay correspondence, that relates three areas in pure mathematics: algebraic geometry, commuative algebra and representation theory of finite groups. Very recently, a McKay correspondence for reflection groups has been established, that relates irreducible representations of finite groups generated by reflections to certain modules over the coordinate rings of the discriminants of these reflection groups. These modules are maximal Cohen-Macaulay modules and can be described by so-called matrix factorizations.
The goal of this project is to explicitly compute (in Macaulay2) matrix factorizations for discriminants of pseudo-reflection groups and so obtain insights that can lead to a better understanding of these objects.


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Description Research collaboration with Colin Ingalls 
Organisation Carleton University
Country Canada 
Sector Academic/University 
PI Contribution E. Faber, S. May (Leeds): Weekly discussions on zoom about matrix factorizations, joint paper with C. Ingalls and his student M. Talarico (Carleton University) in preparation. S. May worked out the case of G(r,p,2).
Collaborator Contribution Computations, discussions.
Impact Joint article about matrix factorizations for G(r,p,n) in preparation. (3 month research placement of PhD student Simon May at Carleton University postponed to Autumn 2021 because of COVID).
Start Year 2021