I have been steeped in the mathematics of General Relativity once again as well as the math up to the Standard Theory and some string theory.

I am at a complete loss as any approach that would find any mapping or provide any theoretic structures to understand one's inner subjective world based on mathematics, geometry, topology, etc. Inner space has no metric, no ruler that would lead to a measurable space or the properties of that space.

Neither can I see any way to go from from subjective space to external space.  They "feel" the same to me and most meditators, but I see no way to explain the outer objective world as a projection of my inner world experience.

There is no entity that is an ego.  Each human has many different talents: ability to judge space, time, movement, kinesthetic, or how to move one's body in space and time, mathematic ability, ability to correctly prioratize tasks, to make accurate assessments of other people's actions, ability to learn and speak a language, etc. These are all executive functions of our minds, and are talents we are not usually aware of because they are us in thre plural.  We are a collection of talents, abilities, learned behaviors, ways of thinking, etc.

The ego, and even the Self, is not like an individual so much when we look closely, but as Nisargadatta said, like a city.  It is like a collection of people, houses, streets, cars, industry, social behaviors, stores, bars, criminals, and lawyers.  We are the same.

Thus to propose some sort of projection mechanism, such that someone says that the world is an illusion, we create or project the world by our thinking, attitudes, or any other suggested mechanism, is just an empty and pointless expression with no suggested mechanisms we can prove through experiment or even theoretically.

Also, I saw more deeply how fragile is the reality of science and the apparent emptiness of string theory, and even before that of quantum mechanics and the more arcane outcomes in General Relativity theory because of all the assumptions one makes to solve Einstein's field equations.

Unless someone has a suggestion of a research tact, I may be dropping this line of exploration soon.