Real Algebra and Geometry

  • Lecturer: Rainer Sinn
  • Date: Tuesdays, 15:15 - 16:45
  • Room: Videobroadcast. Please send an email to Rainer Sinn for the link.


In the field of Real Algebra, the main basic objects are orderings of algebraic structures. We will particularly focus on ordered fields (examples are the rational and real numbers) and see that the set of sums of squares plays a special role in this theory. In particular, we will discuss Artin's solution of Hilbert's 17th problem. We will also study quantifier elimination and basics in semi-algebraic geometry (an example of a tame geometry). Towards the end of the semester, we will also study questions in real algebraic geometry, in particular real questions in classical projective geometry. Prior knowledge in abstract algebra is sufficient. Basics in algebraic geometry and commutative algebra are helpful but not necessary. Materials You will find materials for the course either directly on this website or on Moodle, the learning platform used by the University of Leipzig.

Regular Lectures (Summer 2021)

16.05.2021, 02:30