Rational Elliptic Surfaces and Trigonometry of Non-Euclidean Tetrahedra

University of Chicago

Date(s) : 29/04/2022   iCal
11 h 00 min - 12 h 30 min

I will explain how to construct a rational elliptic surface out of every non-Euclidean tetrahedra. This surface « remembers » the trigonometry of the tetrahedron: the length of edges, dihedral angles and the volume can be naturally computed in terms of the surface. The main property of this construction is self-duality: the surfaces obtained from the tetrahedron and its dual coincide. This leads to some unexpected relations between angles and edges of the tetrahedron. For instance, the cross-ratio of the exponents of the spherical angles coincides with the cross-ratio of the exponents of the perimeters of its faces. The construction is based on relating mixed Hodge structures, associated to the tetrahedron and the corresponding surface.

Zoom: https://univ-amu-fr.zoom.us/j/82958351649?pwd=anBjWUM5enJpMVZFTTl1UEFyTlVzZz09

Meeting ID: 829 5835 1649
Passcode: see email


FRUMAM, St Charles (2ème étage)


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