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Stockholm Master Class in Tropical Geometry

Date: 14 August 2017, 9.00 AM - 27 August 2017, 5.00 PM
Venue: Department of Mathematics, Stockholm University, Department of Mathematics, KTH
Program:  Master Class in Tropical Geometry (pdf 261 kB)

Come to Stockholm and take part in a two week Master Class containing three mini courses in Tropical methods in curve counting and moduli spaces. The Master Class is aimed at PhD students, but also Master level students with profile in algebraic geometry are welcome to participate.

Tropical geometry

Tropical algebraic geometry is a new and rapidly developing area in mathematics, which might loosely be described as a piecewise-linear version of algebraic geometry. The foundational ideas had appeared in different forms in the 1970:s and 80:s, e.g. as Viro's patchworking method, Gelfand-Kapranov-Zelevinsky's amoebas and Maslov's dequantization, but also through work of Bergman, as well as Bieri and Groves. Only since the late 1990:s has an effort been made to systematically exploit connections to questions in classical algebraic geometry, prominently represented in work of Mikhalkin and Sturmfels.

A shining example of the successes of these methods have been to questions in enumerative geometry and mirror symmetry, beginning with a proposal of Kontsevich, actualized by Gross, Mikhalkin, Nishinou, Siebert and others. In recent years, the subject has played a fundamental role in the development of logarithmic Gromov-Witten theory.

Objective and participants

The objective is to give the participants 3 research-oriented crash courses in tropical algebraic geometry, organise them in small groups working on concrete research projects with the ambition of writing student papers in the area which (if their quality will be sufficient) will be posted on arXiv and submitted for publication.

The master class is mainly oriented towards PhD students with interest in algebraic geometry at the beginning of their studies, but also master students whose profile is algebraic geometry might participate.


3 mini courses (5 lectures each) and a number of seminars oriented towards working in concrete research oriented programs in small groups.

Mini courses

  • Enumeration of tropical curves by Hannah Markwig
  • Curve counting in tropical and algebraic geometry by Renzo Cavalieri
  • Curve counting and logarithmic geometry by Dhruv Ranganathan 


Department of Mathematics Stockholm University

Department of Mathematics KTH, Stockholm

Fees and funding

The course is given for free. Junior participants can apply for funding regarding housing in Stockholm during the course.


Renzo Cavalieri, associate professor at Colorado State University
Hannah Markwig, full professor at Universität Tübingen
Dhruv Ranganathan, CLE Moore, Instructor at MIT
Boris Shapiro, professor at Stockholm University

The course is organised in cooperation with and funded by Stockholm Mathemtics Centre.


Apply here!  Last application date is 31:st of March 2017.


Contact: Boris Shapiro

Welcome to Stockholm!