My research interests lay in the realms of Low Dimensional Topology, Contact Topology and Knot Theory. More specifically, I am interested in low dimensional invariants (i.e. invariants of links, 3-manifolds and 4-manifolds) coming from representations of quantum groups, their relationship with other Floer/Gauge-theoretic invariants, and their application to Contact Topology.

I am also interested in categorification. In particular, I am interested in categorified quantum invariants of links (and their possible extensions to 3-manifolds), and categorified quantum spin-networks.

Up to now my research has been focused in the study of transverse link invariants arising from Quantum Homologies (i.e. deformations of Khovanov-Rozansky homologies), and their relationship with other link invariants.

Papers:

Pre-prints:

Transverse invariants from Khovanov-type homologies (arXiv:1705.03481, Submitted)

Combinatorial bounds on transverse and concordance invariants from the deformations of Khovanov homology (arXiv:1707.03424, Submitted)

Transverse invariants from the deformations of Khovanov sl3-homologies and Bennequin-type inequalities (In preparation)

Transverse invariants from equivariant Khovanov-Rozansky homologies and Bennequin-type inequalities (In preparation)

Ph.D. Thesis:

Transverse invariants from the deformations of Khovanov sl2- and sl3-homologies

E-Mail Addresses:
collari[at]math[dot]unifi[dot]it
collari[at]mail[dot]dm[dot]unipi[dot]it