TCC Tropical Geometry
Tropical geometry is an emerging area at the interface between
algebraic geometry and combinatorics. At its most basic it is
(algebraic) geometry over the tropical semiring, where multiplication
is replaced by addition, and addition is replaced by minimum. This
turns polynomials into piecewise-linear functions, and varieties into
In good situations this allows algebro-geometric invariants to be
computed using simpler combinatorics. This has had success in
enumerative geometry, mirror symmetry, Brill Noether theory and
constructing compactifications, among others. See for example
for an illustration of computing Gromov-Witten numbers of the
plane using tropical geometry. See also the first chapter of the
book-draft mentioned below for many more different examples, pictures,
In this module I will introduce the basics of tropical geometry. This
will focus on the elementary algebraic geometry and computational
aspects which are needed in many of the more technical
applications. The first half of the module will not require any
sophisticated algebraic geometry background. While the second half
will require more, it will have more of a survey flavour.
Tropical geometry is not only a subfield of algebraic geometry, but
has deep links to applications. This module will focus on the
algebraic geometry side, but will aim to be accessible to those whose
interests are on the more applied side.
| Diane Maclagan
||B1.35 Zeeman Building (Warwick campus)
|| D.Maclagan at warwick.ac.uk
||(024) 7652 8333
Course Times and Location
|| Your local TCC room
in Bath, Bristol, Imperial, Oxford, or Warwick
| Monday 1pm-3pm
The main reference for this module is the draft book-in-progress I am
writing with Bernd
Sturmfels. A current draft is
This will be updated as the module progresses.
PLEASE send me any typos you notice, no matter how minor. Include in
your email the date of the version containing the typo.
Further references, and a rough outline of the topics to be covered is
available at the schedule page.
There is no formal assessment for this module. Exercises will be
given for each lecture, which will be available on the
Subject to logistics, there will also be a (virtual) seminar at the
end of the term where participants give reports on tropical geometry
papers they have read. This will let you tailor the module to your
particular research interests, and expose you to aspects of tropical
geometry not covered in the module. This will be announced early in the term.