Rational Elliptic Surfaces and trigonometry of Non-Euclidean Tetrahedra

Geometry Luncheon Seminar

Meeting Details

For more information about this meeting, contact Kristin Berrigan, Dmitri Burago.

Speaker: Daniil Rudenko, U Chicago

Abstract: 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.


Room Reservation Information

Room Number: 114 McAllister

Date: 10/30/2019

Time: 12:00pm - 1:30pm