The Langlands program, is a web of connections between number theory and geometry.
Robert Langlands
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.
The geometric Langlands program is a reformulation of the Langlands correspondence.
The geometric Langlands correspondence relates algebraic geometry to representation theory.
Edward Witten
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.