Fundamental Algebra


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


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Defended Theses

  • Statistical instability in chaotic dynamics
      Muhammad Ali Khan (March 2018)
      José Ferreira Alves
  • Profinite topologies on the free group
      Khadijeh Alibabaei (March 2018)
      Jorge Almeida
  •   Rui Manuel Tavares Pinto de Sá Pereira (January 2018)
      Evelina Shamarova
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