Real Algebraic Geometry, Positivity and Convexity

TL;DR

This collection of lecture notes covers real algebraic geometry, positivity, and convexity, including linear matrix inequalities, providing foundational knowledge and insights for students and researchers in the field.

Contribution

It compiles comprehensive lecture notes across multiple courses on real algebraic geometry and convexity, integrating recent topics like linear matrix inequalities.

Findings

Extensive coverage of real algebraic geometry principles.

Introduction to the geometry of linear matrix inequalities.

Accessible educational resource with accompanying video lectures.

Abstract

Chapters 1 to 4 are the lecture notes of my course "Real Algebraic Geometry I" from the winter term 2020/2021. Chapters 5 to 8 are the lecture notes of its continuation "Real Algebraic Geometry II" from the summer term 2021. Chapters 9 and 10 are the lecture notes of its further continuation "Geometry of Linear Matrix Inequalities" from the winter term 2021/2022. These courses have been delivered at the University of Konstanz in Southern Germany. The entirety of these lecture notes is accompanied by a list of 47 long videos which is available from the following YouTube playlist: https://youtube.com/playlist?list=PLbQ93L5pV-a_RRwdEgGungHn5rN43BGe7