I- Introduction to dynamical systems (July 2021- Navember 2021)[Souheib Allout]: In this course, we study examples of dynamical systems from topological and measurable point of vue.
II-Introduction to geometric group theory (July 2021- Navember 2021)[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.
III- Complex analysis (July 2021-October 2022)[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.
IV- Some aspects of Geometry (November 2021-February 2022)[Ghani Zeghib]: Some notes can be found here.