Mathematics, Systems and Robotics Seminar 

07/12/2006, 10:00 — 11:00 — Conference Room, Instituto de Sistemas e Robótica, North Tower, 7th floor, IST
Pedro Resende, CAMGSD/DM

What is a good semigroup of binary relations?

Pseudogroups, inverse semigroups, and groupoids provide generalizations of the mathematical concept of a group that are useful for describing local notions of symmetry, and they are used extensively in differential geometry and operator algebra theory. (Groupoids in particular have already been addressed in this seminar series.) In this talk I shall present a brief introduction to these concepts, taking as a starting point an elementary look at the semigroup of all the binary relations on a fixed set, through which the talk ties up to yet another class of algebraic structures known as quantales. Along the way I shall try to hint at possible connections to application areas such as the control theory of hybrid systems.