Tropical Algebraic Geometry

  • Ilia Itenberg
  • Grigory Mikhalkin
  • Eugenii Shustin

Part of the Oberwolfach Seminars book series (OWS, volume 35)

Table of contents

About this book


Tropical geometry is algebraic geometry over the semifield of tropical numbers, i.e., the real numbers and negative infinity enhanced with the (max,+)-arithmetics. Geometrically, tropical varieties are much simpler than their classical counterparts. Yet they carry information about complex and real varieties.

These notes present an introduction to tropical geometry and contain some applications of this rapidly developing and attractive subject. It consists of three chapters which complete each other and give a possibility for non-specialists to make the first steps in the subject which is not yet well represented in the literature. The intended audience is graduate, post-graduate, and Ph.D. students as well as established researchers in mathematics.


Tropical Geometry algebraic geometry algebraic varieties amoebas enumerative geometry

Authors and affiliations

  • Ilia Itenberg
    • 1
  • Grigory Mikhalkin
    • 2
  • Eugenii Shustin
    • 3
  1. 1.IRMAUniversité Louis PasteurStrasbourg CedexFrance
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada
  3. 3.School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael

Bibliographic information

Industry Sectors
Finance, Business & Banking