Projective Differential Geometry Old and New: From the Schwarzian Derivative to the Cohomology of Diffeomorphism Groups

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Conformal Carroll groups (2014, background): “The Lie algebra cgal + (1 1) 2 clearly admits a non-trivial central extension by , the Virasoro cocycle of the Lie subalgebra S Vect( ) 1 being constructed via the infinitesimal Schwarzian derivative [29] α α ∂ ∂ = ′′′ s t t t dt ( ( ) ) ( ) .”
The Pentagram Map: A Discrete Integrable System (2008, background): “This is a discrete version of the well-known isomorphism between the space of smooth non-degenerate curves in RP2 and the space of linear differential equations, see [17] and references therein and Sect.”
What is wrong with the Hausdorff measure in Finsler spaces (2004, methodology): “The proof of the Crofton formula for hypersurfaces in Finsler spaces, its application to the minimality of totally geodesic hypersurfaces for the Holmes-Thompson volume, and the proof that there is no Crofton formula for the Hausdorff area functional of ϕλ unless λ is zero are all in Section 5”