algebraic analysis

The area of study in algebraic geometry began as a research programme, instigated in 1959 by Japanese mathematician Mikio Sato.

1(algebraic geometry, algebraic topology) The study of systems of linear partial differential equations, using techniques from sheaf theory and complex analysis to examine functions and certain generalisations of functions (such as hyperfunctions and microfunctions).
2Used other than figuratively or idiomatically: see algebraic,‎ analysis.; the use of techniques from algebra (especially elementary algebra) to analyse and solve problems.