Algebra oriented branch of theoretical computer science I have a very strong base in algebra, namely


commutative algebra,
homological algebra,
field theory,
category theory,


and I am currently learning algebraic geometry.

I am a math major with an inclination to switch to theoretical computer science. Keeping the above mentioned fields in mind, which field would be the most appropriate field in theoretical computer science to which to switch? That is, in which field can the theory and mathematical maturity obtained by pursuing the above fields be used to one's advantage?
There have been recent developments in dependent type theory which relate type systems to homotopy types.

This is now a relatively small field, but there is a lot of exciting work being done right now, and potentially a lot of low hanging fruit, most notably in porting results from algebraic topology and homological algebra and formalizing the notion of higher inductive types.