Geometry of SOL-type groups seminar
Next February the 25th I will be delivering a talk about the geometry of SOL like groups at the institute of mathematics, National Autonomous University of Mexico. Talk is free and will be delivered in spanish.
Abstract
In three-dimensional space there are eight possible geometries according to Thurston, one of these geometries is the Sol-type geometry. It is called Sol because the model is a solvable Lie group. The Sol geometry is very particular, there are planes in which the space looks like a Poincaré disk, straight lines are no longer curves that minimize the distance between two points and spheres are not round, to mention a few counter-intuitive characteristics. Recently, Schwartz and Coiculescu have described the geometry of spheres and the regions in which they fail to be smooth surfaces, proving a previous conjecture about volume entropy. The techniques they use work only in three dimensions, so it is an open problem how many of the properties they describe can be generalized. In the talk, the spaces that have the Sol geometry and the limitations to extrapolate these properties to higher-dimensional spaces will be described in more detail.
If you wish, you can find a computer model of Sol and the remaining geometries of space in the direction