Some background: I'vebeen searching for a research project to work through my grad studies and I found information geometry like a strong candidate but the amount of work out there is overwhelming. I would like to see some perspectives on the subject. Maybe some research branches groups may have.
For example: In  they seem to work out Mrugala's idea of thethermodynamic phase space on a smooth manifold but then they turn into something more like numerical analysis.
In the GSI reports one finds alot of information but that is over 3 thousand pages of research and there seems to be a lack of motivational texts about the problems they seem to be hunting.
I have found that goemetric control theory looks like a promising area as well but I couldn't find a useful overview of the subject that maybe overlaps with things being done in information geometry.
Finally, in  they work out what looks like a non-Riemannian framework for information geometry but the theory seems to be quite general and far from a Msc/PhD thesis level. Can anyone point me out in a direction maybe to narrow down the amount of reading material to be covered? thank you very much.
(I would appreciate maybe something pointing in the topological/geometrical data analysis roadmap as well)
 Polysymplectic Geometry of High Order Souriau Lie groups Thermodynamics based on Günther's model, F. Barbaresco.
GSI: Geometric Sicences of Information which are some books result from a conference being done since 2013 every 2 years.