The first call for applications for the new edition of the PhD Program in Mathematics UC|UP (starting September 2019) will be open during January 02, 2019 - February 04, 2019
The prize Eng. António de Almeida for the best doctoral thesis defended at FCUP in the years 2015 to 2017 in the areas of Mathematics, Statistics and Computer Science was awarded to Célia Borlido for her thesis "The word problem and some reducibility properties for pseudo- varieties of the form DRH", supervised by Prof. Jorge Almeida within the scope of PIUDM.
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.