Rational sphere maps: symmetries, gaps, and optimization.

John P. D'Angelo (U Illinois)

Nov 23. 2023, 09:30 — 10:20

We discuss various results pertaining to the possible (minimal) target dimensions of rational sphere maps given various symmetries. We analyze completely what happens when the Hermitian equivariant group (introduced by D'Angelo-Xiao) is the Unitary group, we discuss the gaps for the possible invariant groups (necessarily cyclic), and we discuss an optimization problem whose solution in dimensions 3 or more leads to a symmetrized version of the Whitney map. Precise formulas for the maps in the two-dimensional version of this problem seem intractable, but we provide considerable information about them.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Analysis and Geometry in Several Complex Variables (Workshop)
Peter Ebenfelt (UC San Diego)
Purvi Gupta (IIS Bengalore)
Bernhard Lamel (U of Vienna)
Nordine Mir (Texas A&M U at Qatar)