Martin Gisser
Barvarian hobby mathematician. PhD dropout 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Unpublished theorem of 1996: A complete Riemannian manifold with strict stochasticly positive Ricci curvature is compact and has finite fundamental group.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 KuranishiYamabe), of reducing principal bundle wizardry to prepresheaves 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 RiemannChristoffel 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 wellmentored 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).

Passau, Germany

Member for 9 years, 6 months

18 profile views

Last seen Oct 27 '19 at 1:21
Communities (4)
Top network posts
 27 Is "Cartan's magic formula" due to Élie or Henri?
 27 Riemann's formula for the metric in a normal neighborhood
 19 Which journals publish 1page papers
 6 Applications of Koszul's formula other than the fundamental lemma of Riemannian geometry
 6 Which Bianchi identity is due to Bianchi (or not, since it might be due to Ricci (according to LeviCivita (according to MO))) or vice versa?
 5 Shuffle (co)multiplication and generalized Leibniz formula in tensor calculus
 5 decompose a connection
 View more network posts →
Top tags (1)
Badges (6)
Gold
Silver
Rarest
Bronze
Rarest

Jan 30 '15

Oct 27 '14