Discovery Projects - Grant ID: DP160103897

Funding Activity

Website
http://dataportal.arc.gov.au/NCGP/Web/Grant/Grant/DP160103897

Funding Status
Active

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Funded Activity Summary

Algebraic Schubert geometry and unitary reflection groups. This project aims to generalise the recent work of Elias and Williamson to the complex case. Fundamental to the study of symmetry are the ubiquitous Coxeter groups, which have an associated set of critically important ‘Kazhdan-Lusztig polynomials’. For some Coxeter groups, these may be interpreted in terms of classical geometry, leading to deep positivity properties for their coefficients. Elias and Williamson have recently shown that this geometry may be simulated algebraically for any Coxeter group, so positivity for Kazhdan-Lusztig polynomials holds for all Coxeter groups. This result has explosive consequences in many areas of geometry and algebra. This project is designed to extend these results to complex unitary reflection groups, with potentially dramatic consequences in number theory, representation theory and topology.

Funded Activity Details

Start Date: 01-01-2016

End Date: 01-01-2024

Funding Scheme: Discovery Projects

Funding Amount: $519,300.00

Funder: Australian Research Council

Research Topics

ANZSRC Field of Research (FoR)

Group Theory and Generalisations | Pure Mathematics | Algebraic and Differential Geometry | Algebra and Number Theory

ANZSRC Socio-Economic Objective (SEO)

Expanding Knowledge in the Information and Computing Sciences | Expanding Knowledge in the Mathematical Sciences |

Other Keywords

Algebra and Number Theory | Algebraic and Differential Geometry | Expanding Knowledge in the Information and Computing Sciences | Expanding Knowledge in the Mathematical Sciences | Group Theory and Generalisations | Pure Mathematics

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