Geometry Seminar
Date: October 5, 2015
Time: 3:00PM - 3:50PM
Location: BLOC 220
Speaker: Daniel Brake, Notre Dame
Title: Applications of Monodromy
Abstract: Monodromy action plays an important role in a number of mathematical theories. Stemming from a fundamental principle in complex analysis, the Cauchy integral formula, monodromy loops give all sorts of information about the interior of a region given boundary data. The uses include computing whether a pole is contained in the interior, and determining the breakup of the sheets coming together at a pole. As a consequence, monodromy is used in numerical algebraic geometry to decompose a pure-dimensional set into its irreducible components.
This talk will give an overview of monodromy, and some new connections to algebraic geometry. In particular, we will discuss how to use it to compute some local properties of algebraic varieties, as in the Numerical Local Irreducible Decomposition, and a new method for computing real tropical curves.