Time: 4:00 p.m.
Location: 114 McAllister Building
Name: Adrian Ocneanu
Affiliation: The Pennsylvania State University
Title: Mathematics of symmetry in 4 dimensions - a sculpture
Abstract: We discuss several mathematical topics brought together by the sculpture in our lobby, among others
- regular solids in higher dimensions - why the dimension 4 is special.
- packing spheres in higher dimensions.
- soap bubbles and conformal mappings.
- root systems for Lie algebras - the sculpture illustrates D4, B4, C4 and F4 - their Coxeter elements and the way to read the geometry from the eigenvalues of the adjacency matrix of the graph. Picturing Weyl groups with the sculpure.
- finite subgroups of SU(2) and SO(3) illustrated by the sculpture - the symmetries of the tetrahedron and cube - the E6 affine and E7 affine subgroups of SU(2). The multiplication of symmetries in SU(2) and the corresponding vector fields and fibrations of S3,
and finally
-cutting and folding 3d cardboard kits into 4d solids - an illustrated step by step video guide for 4d kids
