Weil-Petersson perspectives

We highlight recent progresses in the study of the Weil-Petersson (WP) geometry of finite dimensional Teichm\"{u}ller spaces. For recent progress on and the understanding of infinite dimensional Teichm\"{u}ller spaces the reader is directed to the recent work of Teo-Takhtajan. As part of the highlight, we also present possible directions for future investigations.Comment: 18 page