# EP/K035827/1 - Total nonnegativity, quantum algebras and growth of algebras

Research Perspectives grant details from EPSRC portfolio

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Research Perspectives grant details from EPSRC portfolio

Principal Investigator - Sch of Mathematics, University of Edinburgh

Start Date

07/2013

End Date

12/2014

Value

£21,074

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Grant Description

Summary and Description of the grant

This is wide ranging project that involves the three areas of noncommutative

algebra, Poisson algebraic geometry and linear algebra. Also, the solutions

often involve representation theory and combinatorics. In addition, the

project will consider problems concerning growth of algebras.

The development of the theory of quantum algebras was motivated by problems in

Physics from the 1980s onwards. Totally nonnegative matrices have been

involved in problems in such diverse areas as mechanical systems, birth and

death processes, planar resistor networks, computer aided geometric design,

juggling, etc. Results concerning growth of algebras have been obtained from

the 1960s onwards, but the subject was in a quiescent state until the 2000s

when significant advances have been made.

In the past five years, surprising links between the three areas mentioned in

the first paragraph have been discovered and investigated. A partial

understanding of these connections has been gained, especially in the particular

case of coordinate algebras of matrices. The present project aims to further

this understanding by deepening the knowledge of the matrix case and by

expanding the scope of the knowledge to include algebras such as

grassmannians, partial flag varieties and De Concini-Kac-Procesi algebras.

The growth part of the project will concentrate on two specific types of

growth: quadratic growth/Gelfand-Kirillov dimension two, and intermediate

growth (super polynomial, but subexponential).

EPSRC Grants On The Web Link

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Grant Event Details:

Name: Total nonnegativity, quantum algebras and growth of algebras - EP/K035827/1

Start Date: 2013-07-01T00:00:00+00:00

End Date: 2014-12-31T00:00:00+00:00

Organization: University of Edinburgh

Description: This is wide ranging project that involves the three areas of noncommutative
algebra, Poisson algebraic geometry and linear algebra. Also, the solutions
often involve representation theory and combinatorics. In addition, the
project will consider problems ...