Title: Growth rate of 3-manifold homologies under branched covers
Description: Over the last twenty years, a main focus of low-dimensional topology has been on categorified knot invariants such as knot homologies. This dissertation studies the case of two such homologies under the iteration of branched covering maps. In the first part, we find a spectral sequence on the sutured annular Khovanov homology of periodic links of period $r=2^i$. In the second part, we study the asymptotic growth rate of Heegaard Floer homology of cyclic branched covers of a knot as the branching number increases.