PT EN

Fundamental Algebra

Program

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.

 

Research and Events

Events

  • Research Seminar Program (RSP)
    2024/2025
    University of Coimbra, FCTUC, Department of Mathematics, room 2.5
    December 16, 2024
  • PhD Defense
    Rafael Henriques - Numerical methods for the robust reconstruction of elasticity
    Sala José Anastácio da Cunha, Mathematical Building, Largo D. Dinis, Coimbra (14h30)
    January 6, 2025
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Defended Theses

  • Contributions to regularity theory in the calculus of variations
      Vincenzo Bianca (July 2024)
      José Miguel Urbano
  • Higgs Bundles and Geometric Structures
      Pedro Miguel Silva (April 2024)
      Peter Gothen
  • Some aspects of descent theory and applications
      Rui Rodrigues de Abreu Fernandes Prezado (January 2024)
      Maria Manuel Clementino
      Fernando Lucatelli Nunes
More Theses