Izak " Ieke " Moerdijk (born 23 January 1958) is a Dutch mathematician.
Moerdijk studied mathematics, philosophy, and general linguistics and in 1985 at Anne Troelstra his doctorate at the University of Amsterdam ( Topics in Intuitionism and Topos Theory). As a post - graduate student, he was at the University of Cambridge and the University of Chicago. He received a Huygens scholarship from the NWO in the Netherlands in 1986. Since 1988 he was a professor of topology at Utrecht University and he is since 2011 professor of algebra and topology at the Radboud University Nijmegen.
He has been a visiting professor at Cambridge, Montreal, Sydney and Aarhus.
He is co - author of a standard work on topos theory, first published in 1992. Theory, which goes back to Alexander Grothendieck and William Lawvere, has both connections to topology, algebra as well as to logic. He is one of the founders of the algebraic set theory ( Algebraic set theory ) and later turned to algebraic topology and differential geometry, the subject of two of his books. He also dealt with Operaden and constructive non-standard analysis, of which he is one of the founders
More recently (2011) he deals with algebraic structures in quantum information theory.
In 2012 he was awarded the highest Dutch science award, the Spinoza Prize.
- With Saunders MacLane Sheaves in geometry and logic. A first introduction to topos theory, Universitext, Springer- Verlag, 1992, 1994
- Janez Mrčun Introduction to foliations and Lie groupoids, Cambridge Studies in Advanced Mathematics 91, Cambridge University Press 2003
- Gonzalo E. Reyes Models for smooth infinitesimal analysis, Springer- Verlag, 1991
- With André Joyal Algebraic set theory, London Mathematical Society Lecture Note Series 220, Cambridge University Press 1995
- Classifying spaces and classifying topoi, Lecture Notes in Mathematics 1616, Springer Verlag 1995
- With Marius Crainic: Deformations of Lie brackets: cohomological aspects, J. Eur Math Soc. (JEMS ) 10 ( 2008), no.4, 1037-1059.
- Clemens Berger: Axiomatic homotopy theory for operads ", Comment Math Helv 78 (2003 ), no 4, 805-831. .
- Orbifolds as groupoids: an introduction, orbifolds in mathematics and physics (Madison, WI, 2001), 205-222, Contemp. Math, 310, Amer. Math Soc., Providence, RI, 2002.