083 Elias Wegert

Elias Wegert (Technische Universität Bergakademie Freiberg, Germany)// Numerical range, Blaschke products and Poncelet polygons// (Joint work with Ilya Spitkovsky, New York University Abu Dhabi) // Abstract: In 2016, Gau, Wang and Wu conjectured that a partial isometry A acting on a n-dimensional complex Hilbert space cannot have a circular numerical range with a non-zero center. In this talk we present a proof for operators with rank A=n-1 and any n. It is based on the unitary similarity of A to a compressed shift operator generated by a finite Blaschke product B(z). We then use the description of the numerical range by Poncelet polygons associated with zB(z), a special representation of Blaschke products related to boundary interpolation, and an explicit formula for the barycenters of the vertices of Poncelet polygons involving elliptic functions.