Back to Departmental Colloquium: Fall 2009
Departmental Colloquium
Date: Thursday, Nov 5, 2009
Time: 4:15PM
Location: JWB 335
Sam Payne
Stanford University
Title |
Nonarchimedean geometry |
Abstract |
The usual archimedean norm on the complex numbers and its associated analytic geometry (holomorphic functions and differential forms) have been fundamental tools for understanding the geometry and topology of complex algebraic varieties, for instance through Hodge theory and Lefschetz hyperplane theorems, since the beginnings of the subject. Nonarchimedean norms, such as the p-adic norm on the rational numbers, also have an associated analytic geometry which is well-known to number theorists, but this theory is just beginning to be applied in other areas of mathematics, such as algebraic geometry and dynamical systems. This talk will be an introduction to nonarchimedean geometry, through the basic notions of tropicalization and analytification. |
Number Theory
Algebraic Geometry