Research Perspectives - Tools for Visualisation of Portfolios
EPSRC logo

EPSRC Database


Source RCUK EPSRC Data

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

Research Perspectives grant details from EPSRC portfolio

http://www.researchperspectives.org/gow.grants/grant_EPK0358271.png

Professor T Lenagan EP/K035827/1 - Total nonnegativity, quantum algebras  and growth of algebras

Principal Investigator - Sch of Mathematics, University of Edinburgh

Scheme

Overseas Travel Grants

Research Areas

Algebra Algebra

Start Date

07/2013

End Date

12/2014

Value

£21,074

Similar Grants

Automatic generation of similar EPSRC grants

Similar Topics

Topic similar to the description of this grant

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).

Structured Data / Microdata


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 ...