Top-level heading

First person exploration of Thurston’s geometry

Categoria
Colloquium Guido Castelnuovo
Data e ora inizio evento
Data e ora fine evento
Aula
Sala di Consiglio
Sede

Dipartimento di Matematica, Sapienza Università di Roma

Speaker
Rémi Coulon (CNRS, Dijon)
Thurston’s geometrization theorem, proved by Perelman, is a major accomplishment in geometry and topology as it solved the long standing Poincaré conjecture. This theorem states that any reasonable three-dimensional space (i.e. any topological oriented closed three-manifold) can be decomposed into elementary “building blocks” each of which is modeled onto a specific geometry. There are eight such models, now called the Thurston geometries. Some of them can be familiar to us like the Euclidean geometry or the spherical geometry, others are wilder like Nil or Sol. To gain more insight on this topic, we built an app that simulates in real-time what an inhabitant would see in each of these geometries. In this talk we will use this software to introduce Thurston's geometries and illustrate some of their fun features. We will also discuss the mathematical challenges we faced while developing this tool. Joint work with Matsumoto, Segerman, and Trettel.