  The Langlands program is a vast mathematical projection linking number theory
and geometry. In high-energy physics, a connection with mirror symmetry has
been suggested in string theory, but it has been little studied in low-energy
physics. In the framework of the Langlands program, we present a unified
description of the integer and fractional quantum Hall effect and the duality
found in the fractal nature of the energy spectrum of two-dimensional block
electrons, statistical physics, and quantum computation. The new unified view
of existing dualism presented in this paper raises the entirely new question of
how each theory of physics is connected as a piece of the Langlands program.
