## EVENT DETAILS AND ABSTRACT

**Number Theory**
**Title:** Non-Euclidean tetrahedra and rational elliptic surface

**Speaker:** Daniil Rudenko

**Speaker Info:** University of Chicago

**Brief Description:**

**Special Note**:

**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.

**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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