Geometric Langlands correspondence

Robert Langlands, is a Canadian mathematician. 

He is known for his program (formulated in the late 1960s) which is a web of conjectures between representation theory (the branch of mathematics that deals with abstract algebraic structures by representing as linear transformations of vector spaces) and automorphic forms (a well-behaved function) with the study of the Galois group from number theory. 

Langlands won the 2018 Abel Prize for this work. 

Connection to physics:

Anton Kapustin and Edward Witten, in 2007, described a connection between the geometric Langlands correspondence with S-duality of supersymmetric gauge theories.