Centre International de Mathématiques Pures et Appliquées



Ministère Enseignement Supérieur et Recherche, France UNESCO
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Toric methods in geometry, arithmetics and dynamics

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CIMPA-ICTP-CHILE research school

Research School co-sponsored with ICTP

Pontificia Universidad Católica de Chile, Santiago, January 11-22, 2016

In recent years, toric geometry has experienced a rapid growth with a wealth of new results and connections with other areas of mathematics like arithmetic geometry and number theory, dynamical systems, non­ Archimedean and tropical geometry, mirror symmetry and birational geometry, This adds to the more classical connections to combinatorics, computer algebra and singularity theory among others, and applications to areas of science like mathematical biology and chemistry. At the same time, the concrete and explicit nature of toric varieties makes them a perfect entrance door to higher dimensional algebraic geometry.

The main purpose of this research school is to motivate and train Latin American students and young researchers in these subjects. It will consist of 6 courses of 6h each, all of them delivered by well­ recognized specialists from Argentina, USA, France and Spain. These courses will cover a basic introduction to toric varieties, followed by more advanced courses on the topological aspects, singularities, dynamical systems, non­-Archimidean and tropical geometry, and arithmetic geometry of toric varieties. In addition, we plan a series of 10 survey talks delivered by members of our scientific committee and other invited researchers from Latin America, USA and Spain.

Administrative and scientific coordinators

- Martin Sombra, ICREA & Universitat de Barcelona, sombra@ub.edu
- Giancarlo Urzúa, PUC de Chile, gianurzua@gmail.com

Scientific Committee

  • José Ignacio Burgos
  • Javier Fernández de Bobadilla
  • Alicia Dickenstein
  • Javier Elizondo
  • Antonio Laface
  • Alvaro Liendo
  • Sukhendu Mehrotra
  • Ricardo Menares
  • Juan Rivera-Letelier
  • Martin Sombra
  • Giancarlo Urzúa

Local Organizing Committee

Antonio Laface
Alvaro Liendo
Sukhendu Mehrotra
Ricardo Menares
Juan Rivera-Letelier
Giancarlo Urzúa

Scientific Program


  1. Introduction to toric varieties : Alicia Dickenstein (Universidad de Buenos Aires)
  2. Combinatorics and topology of toric varieties : Mircea Mustaţă (University of Michigan)
  3. Introduction to tropical geometry : Sam Payne (Yale University)
  4. Arithmetic intersection theory on toric varieties : Martin Sombra (Universitat de Barcelona)
  5. Toric varieties, their birational modifications and their deformations : Bernard Teissier (Institut Mathématique de Jussieu-Paris Rive Gauche)
  6. The classical n-body problem and its relative equilibria : Alain Albouy (Institut de Mécanique Céleste et de Calcul des Éphémérides)


  • Carolina Araujo (IMPA, Brasil)
  • Michela Artebani (Universidad de Concepción, Chile)
  • Javier Fernández de Bobadilla (ICMAT, España)
  • José Ignacio Burgos (ICMAT, España)
  • Javier Elizondo (Universidad Nacional Autónoma de México)
  • Pedro González-Pérez (Universidad Complutense de Madrid, España)
  • Antonio Laface (Universidad de Concepción, Chile)
  • Álvaro Liendo (Universidad de Talca, Chile)
  • Jenia Tevelev (University of Massachusetts at Amhrest, USA)
  • Mauricio Velasco (Universidad de los Andes, Colombia)

Deadline for registration : October 4, 2015

Application procedure only for applicants not from Chile.

Applicants from Chile must register via local web site :

Voir en ligne : Local web site