# Seminar talk, 9 December 2015

Title: Invariants of projective ${\displaystyle PSL_{2}}$-actions and their application to recognition of fingerprints
We study the field of rational differential invariants of the left ${\displaystyle PSL_{2}(\mathbb {R} )}$-action on the homogeneous space ${\displaystyle \mathrm {Diff} (S^{1})/PSL_{2}(\mathbb {R} )}$ and use them to give an alternative description of the shape space and fingerprints, introduced by Mumford and Sharon.