The first call for applications for the new edition of the PhD Program in Mathematics UC|UP (starting September 2018) will be open during January 02, 2018 - February 02, 2018
The syllabus will vary from year to year but the core syllabus is
- Division rings: Quaternions, Cayley-Dickson construction.
- Wedderburn-Artin Theory: matrix rings over division rings and semisimple modules.
- Tensor products and categories.
- Algebras presented by generators and relations.
- Simple algebras: Weyl algebras, central simple algebras, Brauer group.
Further topics (an uncomplete list):
- Non-commutative polynomial rings: skew-polynomial rings, differential operator algebras
- Lie algebras and their enveloping algebras
- basic facts on Hopf algebras: Frobenius algebras, Maschke theorem, Noetherian Hopf algebras
- Noetherian ring theory: non-commutative localization and Goldie's theorem
- basic facts of homological algebra.