Participate in the online CIMPA/ICTP course by Alvaro Kruger Ramos!


Join Professor Alvaro Kruger Ramos's hybrid course "Geometric Topology of 3-manifolds" from October 24 to 27, 2022.

Professor Alvaro Kruger Ramos is professor at Universidade Federal do Rio Grande do Sul, Brazil.

The course will be taught in english on zoom.

This is a recurring meeting, therefore please register just once for all 4 sessions:

The course will be held on the following days (Attention new schedules) :

  • Monday, 24 October, 02:00 PM - 04:00 PM
  • Tuesday, 25 October, 02:00 PM - 03:45 PM
  • Wednesday, 26 October, 02:00 PM - 04:00 PM
  • Thursday, 27 October, 04:00 PM - 06:00 PM

Abstract: One of the greatest achievements on mathematics in the 21st century is the proof of the Poincaré's Conjecture by Grigory Perelman in 2003. Indeed, Perelman proved a much stronger result, which is the Geometrization Conjecture proposed by William Thurston in 1982. In order to do so, Perelman used the Ricci flow, a geometric/analytical argument proposed by Richard Hamilton. In this course, thought for a student with some background in Riemannian geometry, we will present Poincaré's conjecture in the context of the geometrization, explain the Geometrization theorem together with the eight Thurston's geometries and give an intuitive overview of the proof of Perelman.

Please note that the CIMPA/ICTP courses will be recorded and broadcast on our Youtube channel and on

Programme of other courses

CIMPA does not provide certificates of attendance for online courses.