| Abstract: |
In 50s A. Weil asserted striking analogies in mathematics. He claimed that number theory, which deals with (integral) numbers, theory over finite fields, which deals with algebraic tructures of discrete world, and the theory of complex geometry, which is morally the geometry of where we live, share some analogous properties. This analogy led to a series of conjectures on the existence of "topological theory" for equations over finite fields. These conjectures were proven thanks to contributions of various people, notably Grothendieck and Deligne, but the analogy is still far from being understood, and is still serving as a strong driving force in the field of algebra and geometry. In this lecture, I wish to explain how the philosophy is giving rise to fruitful interactions. |
