Courses
2024-2025
Between mid-October 2024 and mid-February 2025, I am organizing a course in Real Algebraic Geometry, open to Master and Ph.D. students.
Where: University of Leipzig, Paulinum P-701
When: Every Tuesday 11:00-13:00, starting October 15 2024
A tentative list of topics includes:
- Basics on Real Closed Fields
- Intermediate Value Theorem
- Real Puiseux Series
- Real Root Counting
- Semialgebraic Geometry
- Tarski-Seidenberg Theorem
- Curve Selection Lemma
- Boundedness and Closedness
- Triangulations and Stratifications
- Sard and Hardt Theorems
- Topological Properties
- Real Algebraic Curves and Harnack Theorem
- Thom-Milnor Bound
- Algebraic Models of Manifolds
- Basics of Cobordism
- Nash-Tognoli Theorem
Bibliography
- Bochnak, Coste, Roy, Real Algebraic Geometry
- Basu, Pollak, Roy, Algorithms in Real Algebraic Geometry
- Scheiderer, A Course in Real Algebraic Geometry
- Benedetti, Risler, Real Algebraic and Semi-algebraic Sets
- Lerario, Metric Algebraic Geometry
- Mangolte, Real Algebraic Varieties
2023
Between the 19th and 23rd of June 2023 I was lecturer for the compact course Semidefinite Programming for Algebra, Combinatorics and Geometry, together with Sebastian Debus, at the University of Magdeburg.