LAUSR

Michał Kazimierz Heller was born on 12 March 1936 in Tarnów. He holds a chair of philosophy at the Pontifical University of John Paul II in Cracow, Poland, and is an adjunct member of the Vatican Observatory. He is a member of Pontifical Academy of Science. His current research is concerned with the singularity problem in general relativity and the application of noncommutative geometry to physics and cosmology, in particular in seeking the unification of general relativity and quantum mechanics. In 2008 he was awarded the Templeton Prize for Progress Towards Research or Discoveries about Spiritual Realities in appreciation of his dedication at understanding and explaining the interaction of science and religion. He is a Roman Catholic priest and mathematical cosmologist who championes a word view that combines mathematical physics, theology and philosophy. He is the recipient of an honorary degree from Warsaw University of Technology. Since 1987 he cooperates with the group of mathematicians from the Differential Geometry Department of the Warsaw University of Technology. His influence on this group was paramount. Seminars of the group took place in Warsaw and in Cracow interchangeably. Summer and winter seminars were organized in Pasierbiec near Limanowa. The concept of differentiable manifold remains crucial in modelling many physical phenomena. In particular, space-times of all major physical theories are supposed to have the structure of a sufficiently smooth manifold. However, in some areas of research there is a necessity to go beyond this assumption and to consider some generalizations. At the beginning of the cooperation Prof. Heller got an idea to use differential space concept in the sense of Sikorski in order to construct a generalized model of space-time which would possibly contain also classical space-time singularities. The first summer school ’Differential Spaces and Their Applications’ took place in Pasierbiec, 20-26 September 1990. The special issue of the ’Demonstratio Mathematica’ Vol XXIV No 3-4 (1991), contains works presented at this school. In the next period the group was engaged in works concerning a theory of the groupoid model unifying general relativity and quantum mechanics. The group used methods of the noncommutative geometry and considered the convolution algebra of functions on the transformation groupoid over the total space of frame bundle of the space-time with the action of the Lorentz group. They constructed the differential geometry, based on derivation of the algebra end considered the generalized Einstein's equation as the eigenvalue equation for the Einstein operator. Next they investigated the quantum sector of the model representing the algebra in a bundle of Hilbert spaces and obtaining a von Neumann algebra of random operators. This algebra allowed to define the dynamics of random operators by Tomita-Takesaki theorem and to define a noncommutative probability measure (in the sense of Voiculescu's probability theory). It was the idea of Prof. Heller to seek a mathematical structure rich enough to be suitable approximated by the mathematical structures of general relativity and quantum mechanics. The influence of Professor Michał Heller on the group was invaluable. The present issue is dedicated to Prof. Michał Heller in honor of his eightieth birthday.