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Space vectors forming rational angles
Geometry/Topology| Speaker: | Alexander Kolpakov, University of Neuchâtel, Switzerland |
| Location: | Zoom Zoom |
| Start time: | Tue, Jan 25 2022, 1:10PM |
We classify all sets of nonzero vectors in such that the angle formed by each pair is a rational multiple of π. The special case of four-element subsets lets us classify all tetrahedra whose dihedral angles are multiples of π, solving a 1976 problem of J. H. Conway and A. Jones: there are 2 one-parameter families and 59 sporadic tetrahedra, all but three of which are related to either the icosidodecahedron or the root lattice. The proof requires the solution in roots of unity of a -symmetric polynomial equation with 105 monomials (the previous record was only 12 monomials). This is a joint work with Kiran S. Kedlaya, Bjorn Poonen, and Michael Rubinstein.
Join Zoom Meeting https://ucdavis.zoom.us/j/99717970584?pwd=SkVwZG4zeUFvU0hSUmNiSEZuYktvQT09 Meeting ID: 997 1797 0584 Passcode: 204195