Real Algebra and Geometry

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 study the real spectrum in detail.

Date and time info
Tuesday, 13:15 to 14:45

Keywords
Real Algebra, Geometry, Hilbert's 17th problem

Prerequisites
Prior knowledge in abstract algebra is sufficient. Basics in algebraic geometry and commutative algebra are helpful but not necessary.

Audience
Diploma students, PhD students