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
Group actions, Sylow theory. Nilpotent and solvable groups. Free groups and presentations. Lie groups and algebraic groups. Groups with operators. Rings and modules. Hermite, Smith and Jordan normal forms for matrices. Wedderburn theory. Linear representations of groups. Polynomial rings and factorization theory. Field extensions. Galois theory. Norms, traces and discriminants. Ideal theory in commutative rings. Rings of integers. Dedekind domains. Algebraic sets and Hilbert's Nullstellensatz.
The program will cover most of the above topics. Depending on the background and interests of the students, some topics may be developed in considerably more depth than others.