Introduction to Real Algebraic Geometry

Real algebraic geometry is the study of semialgebraic sets, i.e. sets described by polynomial equations and inequalities, and the behaviour of polynomial functions on those sets. A classical and fundamental result is the solution of Hilbert's seventeenth problem by Emil Artin stating that every rational function that is globally nonnegative can be written as a sum of squares of rational functions. In the second part we will look at recent applications of real algebra related to semidefinite programming and polynomial optimization.

Date and time info
Friday 11:15 - 12:45

Keywords
Real algebraic geometry, semialgebraic sets, Hilbert's seventeenth problem, semidefinite programming, polynomial optimization

Prerequisites
linear algebra, basic knowledge in ring and field theory

Audience
MSc students, PhD students, Postdocs

Language
English