Rational Sphere Maps: Symmetries, Gaps, and Optimization

Explore the intricacies of rational sphere maps in this 52-minute lecture by John P. D'Angelo at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the analysis of minimal target dimensions for rational sphere maps with various symmetries. Examine the complete analysis of the Hermitian equivariant group when it is the Unitary group, investigate the gaps for possible invariant groups (which are necessarily cyclic), and consider an optimization problem leading to a symmetrized version of the Whitney map in dimensions 3 or higher. Gain insights into the challenges of deriving precise formulas for maps in the two-dimensional version of this problem, while acquiring substantial information about their properties. This talk, part of the Workshop on "Analysis and Geometry in Several Complex Variables," offers a deep dive into advanced mathematical concepts at the intersection of complex analysis and geometry.