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Details of Grant 

EPSRC Reference: EP/R02300X/1
Title: Foundations and Applications of Tropical Geometry
Principal Investigator: Maclagan, Dr D
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Mathematics
Organisation: University of Warwick
Scheme: Standard Research
Starts: 13 June 2018 Ends: 12 June 2021 Value (£): 326,307
EPSRC Research Topic Classifications:
Algebra & Geometry
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
29 Nov 2017 EPSRC Mathematical Sciences Prioritisation Panel November 2017 Announced
Summary on Grant Application Form
Tropical geometry is geometry over the tropical semiring, which is the usual real numbers with addition replaced by minimum, and multiplication replaced by addition. While the tropical semiring has had applications in optimization and computer science for several decades, the connection to algebraic geometry was first made only at the start of this century. The subject has expanded rapidly in the past decade.

Classically algebraic geometry studies the geometry of the sets of solutions to polynomial equations, called varieties. The fundamentals of algebraic geometry changed dramatically in the 60s with Grothendieck's introduction of schemes. In the first decade of tropical geometry, however, only tropical versions of varieties were considered. This has changed in the past few years, beginning with the work of the Giansiracusas, and of the PI with Rincon, which together introduced a scheme theory into tropical geometry. This allows much more of the power of modern algebraic geometry to be used in tropical geometry.

The primary aim of this project is to further develop the theory of tropical schemes, and apply this technology to problems in algebraic geometry.

The first goal is to develop more of the basic commutative algebra and algebraic geometry of the new theory of tropical schemes. This will then be used to construct tropical versions of important moduli spaces in algebraic geometry, starting with the Hilbert scheme, and use this to address fundamental open questions about the Hilbert scheme. It will also be used to address realizability questions in tropical geometry, which have applications to birational geometry.

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Organisation Website: http://www.warwick.ac.uk