Introduction to Real Algebraic Geometry

  • Lecturer: Mario Kummer
  • Date: Friday 11:15 - 12:45
  • Room: MPI MiS, A3 02
  • Language: English
  • Target audience: MSc students, PhD students, Postdocs
  • Keywords: Real algebraic geometry, semialgebraic sets, Hilbert's seventeenth problem, semidefinite programming, polynomial optimization
  • Prerequisites: linear algebra, basic knowledge in ring and field theory


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.

Regular Lectures (Winter 2016/2017)

15.10.2018, 13:54