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Tropical Differential Geometry

Tropical Differential Geometry

Objective

"The all-pervading utility of differential equations, and therefore of methods for their solution, in mathematics and the physical sciences, especially in mechanical and electronic engineering, is undisputable. The heat and wave equations are star examples. The subject has a long history, including its interactions with modern algebra since it was brought into that framework by Ritt in the late 1930s.

Tropical geometry, introduced two decades ago, is a rapidly developing area of mathematics offering a new approach to algebraic and geometric problems, for instance, counting solutions to equations. ""Tropicalising"" these problems turns them into new problems stated only in terms of ensuring that collections of linear functions are tied for the greatest value, which have the same answers as the originals but can often be easier to solve.

In 2015, the Fellow and others introduced an application of tropical tools to differential algebra. Inspired by the initial successes of these methods, we are here proposing to extend them to classes of differential equation not yet handled,
to bring more algebro-geometric machinery to bear, to transfer further aspects of the theory of tropicalisation of algebraic varieties to differential algebra, and to extend the computational algebra which motivated Grigoriev's interest to our new settings."
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Coordinator

QUEEN MARY UNIVERSITY OF LONDON

Address

327 Mile End Road
E1 4ns London

United Kingdom

Activity type

Higher or Secondary Education Establishments

EU Contribution

€ 195 454,80

Project information

Grant agreement ID: 792432

Status

Ongoing project

  • Start date

    1 June 2018

  • End date

    31 May 2020

Funded under:

H2020-EU.1.3.2.

  • Overall budget:

    € 195 454,80

  • EU contribution

    € 195 454,80

Coordinated by:

QUEEN MARY UNIVERSITY OF LONDON

United Kingdom