1. Introduction to Dynamical Systems (July 2021- November 2021)
Instructor: Souheib Allout
In this course, we study examples of dynamical systems from topological and measurable point of vue.
2. Introduction to Geometric Group Theory (July 2021- November 2021)
Instructor: Lamine Messaci
Topics discussed:
- Finitely presentations of groups, Cayley graphs.
- Free products, amalgamated free products, HNN extensions.
- Some Bass-Serre theory.
- Ends of groups, finiteness properties.
- Hyperbolic groups, CAT(0) spaces.
Main reference: Geometric Group Theory by Cornelia Druțu and Michael Kapovich.
3. Complex Analysis (July 2021-October 2022)
Instructor: Lilia Mehidi
Content:
- Review of basic properties of complex numbers.
- Complex differentiation, Cauchy-Riemann equations, holomorphic functions.
- The Riemann sphere and stereographic projection.
- Complex integration: Path integrals, Cauchy’s theorem.
- General Cauchy’s theorem, Cauchy’s integral formula, Cauchy’s estimate. Liouville’s theorem. Fundamental theorem of algebra. Morera’s theorem.
- Isolated singularities: Removable singularities, poles and essential singularities.
- Power series expansion, holomorphic functions are analytic.
- Holomorphic and meromorphic functions on the Riemann sphere. Laurent series. Order of zeros and poles.
- Residue theorem.
4. Some Aspects of Geometry (November 2021-February 2022)
Instructor: Ghani Zeghib
Some notes can be found here.
