Geometric Structures - Alessandro Tamai - Jan 12 - 4:00 pm (Rome Time)

[Miruna - Stefana Sorea]

Dear All, 

this is a reminder of today's seminar from the series "Geometric
Structures".

Speaker: Alessandro Tamai

Title: Singular solutions spaces of rolling balls problem

Time: January 12, 2021, 4:00 pm (Rome Time) 

Venue: from remote only, on zoom at this link 
https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
[1]
Passcode: geometry

Abstract:  

The "Rolling Balls Model", the model describing a pair of spheres of
different ray rolling one on another without slipping or twisting, is a
classical example of sub-Riemannian problem. The symmetries of the
distribution associated with the system depend on the ratio of the rays
and radically change when the ratio equals 3. Indeed, for this value of
the ratio (and only for this value) it extends to the exceptional simple
Lie group G2 which acts, still for this value of the ratio, also on the
singular solutions related to the problem. 

In this talk we show how it is possible to describe the spaces of such
singular solutions in a geometric way, as a family of 5-dimensional
manifolds depending on the ratio. For rational values of the ratio such
manifolds have a structure of SO(2)-principal bundles which are not
topologically distinguished by their  homology, homotopy and de Rham
cohomology groups. In addition, we show that for integer values of the
ratio the configuration manifold of the problem is a branched covering
of each of such manifolds and how the covering maps associated allow to
relate them with another known family of topological spaces, the lens
spaces.  

This talk is based on the research works developed in my master thesis
at University of Trieste, under the supervision of the professor
A.Agrachev. 
More information can be found here:
https://sites.google.com/view/geometric-structures/ [2] 

Everyone is welcome! 
-- 
_Miruna-Stefana Sorea_
_Postdoctoral Researcher_
_Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste,
Italy_
_HTTPS://SITES.GOOGLE.COM/VIEW/MIRUNASTEFANASOREA/_ 

Links:
------
[1]
https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
[2] https://sites.google.com/view/geometric-structures/