- Lecturer: Daniele Agostini
- Date: Thursday, 17:15 - 18:45
- Room: Videobroadcast via Zoom. Please send an email to Daniele Agostini for the link.
- Prerequisites: Commutative algebra and algebraic geometry at an undegraduate level
- Remarks: Attendance is free but registration is required. To register or for any other information contact Daniele Agostini.
AbstractThe idea of this reading group is to develop the basic notions of modern algebraic geometry, through the language of schemes. References: We will follow closely the wonderful lecture notes by Vakil:
- R. Vakil, Foundations of Algebraic Geometry.
- R. Hartshorne, Algebraic Geometry. Springer.
- Q. Liu, Algebraic Geometry and Arithmetic Curves. Oxford University Press.
- D. Eisenbud and J. Harris, The geometry of schemes. Springer.
- U. Görtz and T. Wedhorn, Algebraic Geometry I: Schemes. Springer.
- A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique. Publications Mathématiques de l'IHÉS.
- The Stacks project authors, The Stacks project.
- Lecturer: Rainer Sinn
- Date: Tuesdays, 15:15 - 16:45
- Room: Videobroadcast. Please send an email to Rainer Sinn for the link.
AbstractIn 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.
- Lecturers: Paul Breiding, Jürgen Vollmer, Eckehard Olbrich
- Date: 10.15 - 11.40 (Tuesdays), see schedule for dates and more info
- Room: Videobroadcast via Zoom.