I have a very strong base in algebra, namelycommutative 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?
Algebra oriented branch of theoretical computer science
soft question;algebra;advice request;ct.category theory