  Topological transitions in electronic band structures, resulting in van Hove
singularities in the density of states, can considerably affect various types
of orderings in quantum materials. Regular topological transitions (of neck
formation or collapse) lead to a logarithmic divergence of the electronic
density of states (DOS) as a function of energy in two-dimensions. In addition
to the regular van Hove singularities, there are higher order van Hove
singularities (HOVHS) with a power-law divergences in DOS. By employing
renormalization group (RG) techniques, we study the fate of a spin-density wave
phase formed by nested parts of the Fermi surface, when a HOVHS appears in
parallel. We find that the phase formation can be boosted by the presence of
the singularity, with the critical temperature increasing by orders of
magnitude. We discuss possible applications of our findings to a range of
quantum materials such as Sr$_3$Ru$_2$O$_7$, Sr$_2$RuO$_4$ and transition metal
dichalcogenides.
