Bourgain's work touches on several central topics of mathematical analysis: the geometry of Banach spaces, convexity in high dimensions, harmonic analysis, ergodic theory, and finally, nonlinear partial differential equations from mathematical physics.
Bourgain ng trabaho touches sa ilang mga sentral na paksa ng matematikal na pagsusuri: ang geometry ng Banach puwang, katambukan sa mataas na sukat, maharmonya analysis, ergodic teorya, at sa wakas, nonlinear bahagyang kaugalian equation mula sa matematika physics.