Number Theory

Title: Non-Euclidean tetrahedra and rational elliptic surface
Speaker: Daniil Rudenko
Speaker Info: University of Chicago
Brief Description:
Special Note:

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.

Date: Monday, November 05, 2018
Time: 4:00PM
Where: Lunt 107
Contact Person: Bao Le Hung
Contact email: lhvietbao@math.northwestern.edu
Contact Phone:
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