报告题目：Noncommutative Dynamical Geometry and Reality
报告人：Fred Van Oystaeyen
摘要：If you want noncommutative geometry to apply to reality you have to make a noncommutative version of space-time . Since in relativity theory the curvature of space is influenced by gravity that geometry has to be dynamical, ie. change in time. So I start from an axiomatic definition of noncommutative geometry and make it vary over time. There is a notion of commutative shadow of a noncommutative geometry defined by places with trivial self-intersection (in the noncommutative space there are many places with non-trivial self-intersection. Under some minimal "continuity" assumptions one can construct a dynamical commutative geometry (in physics you can assume this is at each moment analytically isomorphic to usual space-time!) I construct temporal points and a "moment space" at each moment which turns out also to be a commutative geometry . From the dynamical sheaf theory on my notion of noncommutative space one obtains a description of the stalk at some temporal point of the noncommutative sheaf in terms of the stalk at the corresponding point in the moment space . This states that the noncommutative sheaf on the noncommutative space is determined by the commutative theory on the moment space (but that is a space of higher dimension !) . The model obtained allows some elegant explanation of quantum phenomena ,the talk will end with some remarks about the meaning of the assumption that our reality is in a dynamical noncommutative geometry,including some Physics eg the double slit experiment.
Prof Van Oystaeyen is emeritus at the university of Antwerp. He started long lasting project on the Brauer group, the noncommutative scheme theory of associative algebras, graded rings and projective geometry. He published over 300 scientific publications including one on Botany and a proceedings on Robotics. He also pioneered a theory of noncommutative space with some new ideas for Physics. Many European research projects of the EC and the ESF were organized by him but also education projects in Mathematics like Erasmus,Tempus,.... He also organized or co-organized More than 50 international meetings in many countries and guided about 40 Ph.D. students. He was honorary professor at Beijing Normal University, and obtained the Doctor Honoris Causa degree at the university of Almeria (Spain).