Richard Wentworth, Johns Hopkins U., USA

Harmonic Maps to the Weil-Petersson Completion of Teichmueller Space

The talk will review the structure of the metric completion of Teichmueller space with respect to the Weil-Petersson metric as a nonpositively curved Alexandrov space. Harmonic maps with Teichmueller space as a target may be used to study representations of fundamental groups into mapping class groups. A regularity result for the case of two dimensional domains will be discussed.