Thesis DefenseMonday July 29th, 2019 Time: 2:00 PM Title: Invariants of transverse and annular links in combinatorial link Floer homology Speaker: Apratim Chakraborty, Stony Brook University Location: Math Tower 5-127 Abstract: In this dissertation, we explore the Ozsvath-Szabo-Thurston transverse invariant and various concordance invariants that could be defined using combinatorial link Floer homology. We prove that non-vanishing of the transverse invariant for a link is equivalent to non-vanishing of the invariant for certain transverse cables of that link. As an application, to these results we generate many infinite families of examples of Legendrian and transversely non-simple topological link types. Then, we give a refinement of the transverse invariant. Finally, we define an annular concordance invariant and study its properties. When specialized to braids, this invariant gives bounds on band rank. We also study the relationship of this invariant with transverse and braid monodromy properties.