Semigroups

Recommended Prerequisites

Basic background in Mathematics, including an introduction to Abstract Algebra and basic knowledge of General Topology. 

Teaching Methods

Lectures have an expository character, leaving sufficient room for students’ participation. As an integral part of the learning process, numerous exercises are recommended.

Learning Outcomes

The course unit is intended to introduce the theory of semigroups. The students should come to understand the motivation for the theory and its connections with Abstract Algebra in general, where it looks for methods and inspiration, and with Theoretical Computer Science, where it finds problems, techniques, and applications. They should also realize how the profinite perspective enriches the theory and allows a more sophisticated mathematical handling of problems which at their genesis have an essentially combinatorial character.

Work Placement(s)

No

Syllabus

The course explores some of the various approaches to the theory of semigroups: algebraic, combinatorial, dynamical, geometric, language-theoretic, numerical or profinite. The specific subclasses of semigroups to be studied may include finite, inverse, numerical or profinite semigroups, as well as groups. 

Assessment Methods

Assessment
Resolution Problems: 100.0%

Bibliography

J. Almeida, Finite Semigroups and Universal Algebra, World Scientific, 1995.

J. Almeida, Profinite Semigroups and Applications, in V. Kudryavtsev, I. G. Rosenberg (eds.), Structural Theory of Automata, Semigroups, and Universal Algebra, Proc. NATO Adv. Study Institute, Montréal, 2003. Springer, 2005, 1-45.

J.-E. Pin, Varieties of Formal Languages, Plenum, 1986.

J. Rhodes and B. Steinberg, The q-theory of Finite Semigroups, Springer Monographs in Mathematics, 2009.