# EP/I008071/1 - Tropical Geometry

Research Perspectives grant details from EPSRC portfolio

EPSRC Database

Source RCUK EPSRC Data

Research Perspectives grant details from EPSRC portfolio

Principal Investigator - Mathematics, University of Warwick

Start Date

06/2011

End Date

10/2014

Value

£284,238

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

Tropical geometry is an emerging area of algebraic geometry in which a variety is studied via its combinatorial shadow, known as the tropical variety. At its most basic, tropical geometry is geometry over the tropical semiring, where multiplication is replaced by addition and addition is replaced by minimum. Tropical polynomials are thus piecewise linear functions: 3x^2+2y^2 becomes min(2x+3,2y+2).A (complex affine) algebraic variety is the set of common solutions in the complex numbers to a set of polynomial equations. Tropical geometry turns a variety into a polyhedral fan, called the tropical variety, which is a combinatorial object.The overarching aim of this project is to determine which invariants of a variety can be computed from its tropical variety. In particular, the first goal of the project is to determine when the nef and effective cones of a variety can be determined via tropical methods. These cones are an important invariant of the variety coming from birational geometry. The second goal of the project is to understand when the Chow or cohomology rings of the variety can be determined from the variety. The final goal is to apply this understanding to the tropical space of stable maps, by realizing these spaces as tropicalizations of the original spaces.

EPSRC Grants On The Web Link

http://gow.epsrc.ac.uk/NGBOViewGrant.aspx?GrantRef=EP/I008071/1

Structured Data / Microdata

Grant Event Details:

Name: Tropical Geometry - EP/I008071/1

Start Date: 2011-06-01T00:00:00+00:00

End Date: 2014-10-31T00:00:00+00:00

Organization: University of Warwick

Description: Tropical geometry is an emerging area of algebraic geometry in which a variety is studied via its combinatorial shadow, known as the tropical variety. At its most basic, tropical geometry is geometry over the tropical semiring, where multiplication is rep ...