About that math
This is the reply I got from a math professor at MIT when I asked him about sub-Riemannian manifolds:
Unfortunately I'm leaving tomorrow morning for the break, and will be travelling during much of IAP. Also, I really don't know anything about sub-Riemannian manifolds or other degenerate metrics. I'm sorry to say that sub-Riemannian geometry is a very specialized branch of geometry, unfamiliar to most geometers, even those who do Riemannian geometry for a living (which isn't really my case). So I'm not sure if we have anyone at MIT who'd be an expert on that. Still, perhaps you could try asking someone in our department who's closer to Riemannian geometry: among the senior faculty there's (name removed) but he's probably hard to catch during the break; among more junior people (postdocs) I'd suggest (person 1) or (person 2) though I'm not sure how familiar any of them would be with sub-Riemannian structures.
So I have now confirmed that I am actually studying a branch of math that MIT math professors don't know anything about. On the plus side, this might make it easier for me to convince my thesis committee that just finding the geometrical properties of the manifold will actually be sufficient for a PhD.
Unfortunately I'm leaving tomorrow morning for the break, and will be travelling during much of IAP. Also, I really don't know anything about sub-Riemannian manifolds or other degenerate metrics. I'm sorry to say that sub-Riemannian geometry is a very specialized branch of geometry, unfamiliar to most geometers, even those who do Riemannian geometry for a living (which isn't really my case). So I'm not sure if we have anyone at MIT who'd be an expert on that. Still, perhaps you could try asking someone in our department who's closer to Riemannian geometry: among the senior faculty there's (name removed) but he's probably hard to catch during the break; among more junior people (postdocs) I'd suggest (person 1) or (person 2) though I'm not sure how familiar any of them would be with sub-Riemannian structures.
So I have now confirmed that I am actually studying a branch of math that MIT math professors don't know anything about. On the plus side, this might make it easier for me to convince my thesis committee that just finding the geometrical properties of the manifold will actually be sufficient for a PhD.