Topology, Geometry and Singularity Theory

This one-year taught masters course in mathematic provides an advanced training in topology, algebraic geometry and singularity theory. It is an excellent preparation for mathematical research and will enable the student to proceed to the forefront of knowledge in one of these fields.

Program:

• A two weeks intensive program, consisting of two courses:

  1. Algebraic Topology: fundamental group, coverings, singular homology (B. Audoux, D. Moussard)

  2. Differential Geometry: differential manifolds, vector bundles, tangent spaces, locally trivial fibrations, Ehresmann Theorem (A. Pichon)

• A first semester consisting of the following courses, 25 hours each:

  1. Low Dimensional Topology: 3-manifolds, knot theory (B. Audoux, D. Moussard)

  2. Real Algebraic Geometry: Tarski-Seidenberg Theorem, semi-algebraic sets, o-minimal structures, cellular decompositions, triangulations (G. Comte, G. Rond)

  3. Introduction to Complex Analytic Geometry: holomorphic functions in several variables, analytic sets, local theory, proper maps, sheaves (A. Teleman)

• A second semester consisting of the following courses, 25 hours each:

  1. Geometry of the complex singular sets: conical structure Theorem, Milnor Fibration, monodromy, resolution of singularites of complex curves and surfaces (A. Pichon)

  2. Local algebraic theory of singularities: algebraic properties of power series, examples: algebraicity, finite determined hypersurfaces, quasi-ordinary singularities (G. Rond)

  3. Topology of real algebraic varieties (F. Mangolte)

• A Master thesis. Supervised by a professor and/or researcher, each student will work on a research project on a specialization topic of their choice. This work will lead to a written Master thesis and it will be presented in a seminar.

• Additional parts:

A student seminar: from September on, every week there will be a presentation by either a student in the program, or a member of the research group, on a topic that is related to the topics of the program.

There will be opportunities to take language classes in French and/or in English, depending on needs.

Registration starts in March: https://sciences.univ-amu.fr/fr/candidatures-inscriptions

You also have to send your CV to guillaume.rond@univ-amu.fr.