Recruitment Talk: Angelica Cueto

math_sculpture
December 15, 2014
2:00 pm - 3:00 pm
CH240

Date Range
2014-12-15 14:00:00 2014-12-15 15:00:00 Recruitment Talk: Angelica Cueto Title: Non-Archimedean CombinatoricsAbstract:  Non-Archimedean analytic geometry, as developed by Berkovich, is a variation of classical complex analytic geometry for non-Archimedean fields such as p-adic numbers. Solutions to a system of polynomial equations over these fields form a totally disconnected space in their natural topology. The process of analytification adds just enough points to make them locally connected and Hausdorff. The resulting spaces are technically difficult to study but, notably, their heart iscombinatorial: they can be examined through the lens of tropical and polyhedral geometry.I will illustrate this powerful philosophy through concrete examples, including elliptic curves, the tropical Grassmannian of planes of Speyer-Sturmfels, and a compactification of the well-known space of phylogenetic trees of Billera-Holmes-Vogtmann.This talk is based on joint works with M. Haebich, H. Markwig and A. Werner. CH240 America/New_York public

Title: Non-Archimedean Combinatorics

Abstract:  Non-Archimedean analytic geometry, as developed by Berkovich, is a variation of classical complex analytic geometry for non-Archimedean fields such as p-adic numbers. Solutions to a system of polynomial equations over these fields form a totally disconnected space in their natural topology. The process of analytification adds just enough points to make them locally connected and Hausdorff. The resulting spaces are technically difficult to study but, notably, their heart is
combinatorial: they can be examined through the lens of tropical and polyhedral geometry.

I will illustrate this powerful philosophy through concrete examples, including elliptic curves, the tropical Grassmannian of planes of Speyer-Sturmfels, and a compactification of the well-known space of phylogenetic trees of Billera-Holmes-Vogtmann.

This talk is based on joint works with M. Haebich, H. Markwig and A. Werner.