## SPESSATO STEFANO

PhD Student**PhD program:**: XXXIII

**tutor**: G. Mondello

**advisor**: P. Piazza

I am a Ph.D. student in Differential Geometry and Analysis on manifolds. My research topic is about to define a secondary index for the signature operator of non-compact Riemannian manifolds and to study its properties.

In particular, the main goal is to give a proof for an equivalent version of the secondary index theorem, that holds for partitioned PSC spin manifolds. The consequences of this study could give useful tools to classify proper homotopy equivalences between differential manifolds.