SAMS Subject Classification Number: 29

A congruence is a fundamental and essential tool in algebra. It will be shown that a congruence can also be defined for non-algebraic mathematical objects, leading to the natural counterparts of the algebraic isomorphism theorems, subdirect products and Birkhoff’s Theorem. In particular, this theory of non-algebraic congruences provides the last missing piece of the puzzle that completes the full correspondence between the radical theory of algebraic structures and the theory of connectednesses and disconnectednesses of topological spaces and graphs. However, as we shall see, it also brought some unexpected differences between the algebraic and the non- algebraic radical theories to the fore.

Bio: Stefan Veldsman started his academic career in 1977 as a junior lecturer at the University of Port Elizabeth (now called Nelson Mandela University). With a life in academia, he held teaching and research positions at the University of Port Elizabeth, the Rand Afrikaans University (now the University of Johannesburg), Sultan Qaboos University (in Muscat, Oman) and a short term visiting professor position at the Technical University in Vienna.

In September 2019, he retired from the Nelson Mandela University where he is now Emeritus Professor. Since January 2020 he is also an Honorary Research Fellow at the School of Engineering and Mathematical Sciences, La Trobe University (Melbourne).