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The mathematical ties between South Africa and Leiden: Marcel de Jeu professor by special appointment at the University of Pretoria

A long-term mathematical collaboration between South Africa and Leiden will continue with the appointment of Marcel de Jeu as professor by special appointment at the University of Pretoria. He will be working in the field of Positivity.

In addition to his work in Leiden, De Jeu has an appointment as adjunct visiting professor at the University of Mississippi and a guest appointment in Delft. In Pretoria, he has been appointed in the group of abstract analysis, topology and applications. De Jeu describes himself as a functional analyst, working on the area of ‚Äč‚Äčanalysis that deals with the study of topological vector spaces and continuous operators between such spaces. 'Within that, I spend most of the time in the field of Positivity: the theory of ordered functional analytic structures and their applications.'

Illustration of De Jeu's work: the positive cone in a three-dimensional ordered space and the image thereof under a positive operator and under the square of that positive operator.

De Jeu focuses mainly on a certain group of ordered vector spaces: Banach lattices. 'I am developing a theory of positive representations of groups and ordered Banach algebras on Banach lattices.' Analogous work within the context of Hilbert spaces goes back to the days of the famous Hungarian-American mathematician John von Neumann (1903-1957). 'I expect that the collaboration with Pretoria will certainly be fruitful for this work. But it will also benefit other topics within Positivity that I am working on, such as the study of lattices of continuous functions.'

Historical ties

The ties between Leiden and South African functional analysts go way back, says De Jeu. They originated in the fifties of the twentieth century, when Zaanen was professor of mathematical analysis in Leiden. Of his thirteen PhD students, several came from South Africa; at that time it was customary for African-speaking academics from that country to want to obtain a PhD in the Netherlands. Several of Zaanen's PhD students later became professors in South Africa, and Dutch PhD students of Zaanen's such as Huijsmans and De Pagter in turn maintained close ties with South African colleagues. These connections have continued ever since.

Positivity community

De Jeu has many contacts in the international Positivity community, including South African colleagues. Two of his PhD students have been appointed at the University of Pretoria: Marten Wortel and Miek Messerschmidt. In addition, he collaborates with Jan Harm van der Walt, who has recently been appointed associate professor in Pretoria and is also a colleague within Positivity. 'He spent two months in Leiden with his family with two small children during a sabbatical in May and June 2017.' These contacts, together with meetings at conferences and workshops over the years with other analysts from Pretoria and South Africa, eventually led to to De Jeu's appointment in Pretoria.

South Africa leading in Positivity

'My work fits very well with what is happening in Pretoria. There are a number of people who work very close to me within Positivity. And there is a strong functional analytic tradition in Pretoria overall. Functional analysis is well represented throughout the country, and for Positivity, South Africa is even the strongest in the world. Additional contacts with other universities in South Africa, for example the University of Johannesburg or University of The Witwatersrand, are therefore possible, De Jeu thinks. De Jeu: 'I nowadays feel quite at home in South Africa - although social inequality remains painful to see - and I was also a keynote speaker at workshops.' He plans to stay in Pretoria for a few more weeks in July, as a speaker at the bi-annual Positivity congress and for research collaboration.

Education and student exchange

He will also be involved in education there. 'When I will be in Pretoria for a longer period of time, I might start teaching more specialised courses, in cooperation with the staff over there. A course on Banach lattices, for example. Joint supervision of master's theses is also an option.'

A Memorandum of Understanding already exists between Leiden and Pretoria regarding student exchange. 'Leiden has money available for this: a scholarship for a year or two scholarships for six months. We will now be able to implement this more easily.' 

De Jeu has also filed an application in the Erasmus+ International Credit Mobility Programme for staff and student exchange between Pretoria and Leiden. And he wants to try to have the South African National Research Foundation fund joint PhD students. 'This contact also provides, apart from possible funding from the NRF, the possibility to scout talent in Pretoria. In South Africa it is encouraged to do a master's or PhD track outside the country, and then come back. This appointment will help greatly in getting that talent to Leiden. '

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