Differential Geometry

Program Overview

Program Overview:

This Master’s program provides advanced training in a fundamental area of mathematics, namely Differential Geometry and its Applications. Upon completion of this Master’s degree, graduates are qualified to undertake teaching duties at both secondary and university levels. They may also apply for doctoral studies in Mathematics, particularly in fields such as Differential Geometry, Nonlinear Analysis on Manifolds, Riemannian Geometry, Lie Algebra, and Topology.

Main Areas of Study:

· Fundamental geometry: Differential geometry (Riemannian, manifolds), algebraic geometry, complex geometry, topology.

· Geometry and Computer Graphics (CG): 3D modeling, geometric processing algorithms, rendering, virtual/augmented reality.

· Mathematics and Applications: Connections with algebra, analysis, and partial differential equations

Skills Acquired:

Curve Analysis: Study of uniform curves, arc length, reparameter regression, and normalized parametric representation, as well as the Frenet-Séré equations.

Surface Theory: Understanding of simple surfaces, coordinate changes, the tangent vector, the first and second fundamental formulas, and the Weingarten diagram.

Advanced Differential Geometry: Understanding of geodesic curves, Gaussian curvature, and mean curvature.

Topology and Applications: Ability to work with differentiable manifolds and applications of Riemannian and pseudo-Riemannian geometry.

Teaching Language : Français

Curriculum Highlights

Core Courses

• Differential Manifolds: Study of local and global structures, maps and atlases, smooth functions.

• Tangent and Cotangent Bundles: Tangent space, vector fields, differential forms.

• Differential Calculus: Exterior derivatives, Lie derivatives, the concept of curvature.

• Geometry of Curves and Surfaces: Curvature, torsion, metric, geodesics.

• Integration and Stokes' Theorem: Integration of differential forms on manifolds.

• Lie Groups: Introduction to transformation groups.

Advanced Topics

• Riemannian Geometry: The study of manifolds equipped with a metric, including curvature tensors, connections, and geodesics.

• Lie Groups and Algebras: Analysis of continuous symmetries on manifolds.

• Differential Topology: The study of the topological properties of manifolds, including Morse theory and characteristic classes.

• Geometric Analysis: Application of partial differential equations (PDEs) to geometry, such as the Ricci flow.

• Symplectic/Kählerian Geometry: Fundamental structures for classical mechanics and complex geometry.

• Applications in Mathematical Physics: Geometric formalism for general relativity and gauge theory.

Differential Geometry

Program Overview

Program Overview:

Main Areas of Study:

· Fundamental geometry: Differential geometry (Riemannian, manifolds), algebraic geometry, complex geometry, topology.

· Geometry and Computer Graphics (CG): 3D modeling, geometric processing algorithms, rendering, virtual/augmented reality.

· Mathematics and Applications: Connections with algebra, analysis, and partial differential equations

Skills Acquired:

Curve Analysis: Study of uniform curves, arc length, reparameter regression, and normalized parametric representation, as well as the Frenet-Séré equations.

Surface Theory: Understanding of simple surfaces, coordinate changes, the tangent vector, the first and second fundamental formulas, and the Weingarten diagram.

Advanced Differential Geometry: Understanding of geodesic curves, Gaussian curvature, and mean curvature.

Topology and Applications: Ability to work with differentiable manifolds and applications of Riemannian and pseudo-Riemannian geometry.

Curriculum Highlights

Core Courses

• Differential Manifolds: Study of local and global structures, maps and atlases, smooth functions.

• Tangent and Cotangent Bundles: Tangent space, vector fields, differential forms.

• Differential Calculus: Exterior derivatives, Lie derivatives, the concept of curvature.

• Geometry of Curves and Surfaces: Curvature, torsion, metric, geodesics.

• Integration and Stokes' Theorem: Integration of differential forms on manifolds.

• Lie Groups: Introduction to transformation groups.

Advanced Topics

• Riemannian Geometry: The study of manifolds equipped with a metric, including curvature tensors, connections, and geodesics.

• Lie Groups and Algebras: Analysis of continuous symmetries on manifolds.

• Differential Topology: The study of the topological properties of manifolds, including Morse theory and characteristic classes.

• Geometric Analysis: Application of partial differential equations (PDEs) to geometry, such as the Ricci flow.

• Symplectic/Kählerian Geometry: Fundamental structures for classical mechanics and complex geometry.

• Applications in Mathematical Physics: Geometric formalism for general relativity and gauge theory.

Admissions Information

- Bachelor's degree in Mathematics (LMD system)

- Bachelor's degree (old system)

- Postgraduate Diploma