The program aims lead the student the cutting edge of research in a given specialty and make it an independent researcher. Along the way, student will have the opportunity to sharpen his critical thinking and cultivate his originality of thought, as well as to exert his creative talents, in a way that will help student to be able to contribute by his work the advancement of science. Areas of expertise: algebra, analysis, differential geometry, logic and foundations, applied mathematics, number theory and probabilities.