Geometric Langlands Program
The Geometric Langlands Program is a branch of mathematics that connects number theory, geometry, and representation theory. It seeks to establish deep relationships between modular forms, algebraic geometry, and quantum field theory. The program aims to understand how certain mathematical structures can be transformed and related to one another.
At its core, the program involves studying sheaves and D-modules on algebraic curves. This approach allows mathematicians to explore the symmetries and dualities of various mathematical objects, leading to new insights in both pure mathematics and theoretical physics. The Langlands correspondence is a key aspect of this program, linking different areas of mathematics.