Member for 8 years, 1 month
Last seen more than 1 year ago
Barvarian hobby mathematician. PhD drop-out for many reasons last century, but actually can't let go of math.
Interested in Riemannian analysis/geometry - doing it my way...
Unpublished theorem of 1996: A complete Riemannian manifold with strict stochasticly positive Ricci curvature is compact and has finite fundamental group. (Exact formulation and 1 page logarithmic Sobolev proof to be written up one day. I still owe this to KD Elworthy...)
Ever since I'm on the quixotic quest of eliminating vector field brackets from tensor calculus (except e.g. submersion curvature), spurious occurences of Jacobi fields from basic differential geometry, or of Frobenius's theorem (except in Freudenthal's simplification if Kuranishi-Yamabe), of reducing principal bundle wizardry to pre-presheaves plus frame parallel transport, etc. and perhaps other abstract obsessions.
More constructively I'm trying to put Riemannian geometry from the head on its feet, starting with Zariski's cotangent bundle on locally ringed space with a Riemann-Christoffel formula on differentials.
My hero in wielding Occam's razor (like the Death clock in the Stiftskirche of Altötting (where I first learned math as a well-mentored autodidact) is Albert Einstein. https://de.wikipedia.org/wiki/Tod_von_Alt%C3%B6tting He stresses an important caveat: Do not oversimplify. Tensor calculus can be simplified by not simplifying away basic functor stuff. Thus in my way of tensor(-Hom) calculus tangent space is the double dual of classical tangent space - reflecting a fundamental distinction of differential geometry from algebraic geometry: Torsionless modules (for which Zariski cotangent space is the universal differential module).