Research group:
Noncommutative Topology and Geometry of Quantum Fibrations
7 - 10 May, 2012, Warsaw
Organizer
- Piotr M. Hajac
Programme
MONDAY, 07 May, 2012 (IMPAN, room 322, IIIrd floor)
10:15 Simon Brain (Universite du Luxembourg)
NONCOMMUTATIVE DIFFERENTIAL GEOMETRY OF A QUANTUM DEFORMATION OF THE 7-DIMENSIONAL HOPF FIBRATION
For well over a decade it has been an open problem to find a q-deformed analogue of the principal SU(2) Hopf fibration of the 7-dimensional sphere equipped with finite-dimensional noncommutative differential structures. In the litearture one finds a range of examples of such quantum 'quaternionic' Hopf fibrations, but only at the level of infinite dimensional 'universal' differential structures. In this talk I will present an example of a q-deformed quaternionic Hopf fibration whose total space and base space are equipped with finite-dimensional differential structures. By investigating the quantum symmetries of the fibration, I will describe the geometry of the corresponding quantum twistor space (i.e. a noncommutative 3-dimensional complex projective space) and use it to study a system of anti-self-duality equations on the base space quantum 4-dimensional sphere. The system of equations admits a canonical 'instanton' solution coming from a natural projection defining a noncommutative vector bundle over this quantum sphere. (Joint work with G. Landi).
14:15 Elmar Wagner (Universidad Michoacana de San Nicolas de Hidalgo, Morelia, Mexico)
A NON-COMODULE-ALGEBRA EXAMPLE OF THE PULLBACK OF PRINCIPAL COACTIONS
The class of principal coactions is closed under one-surjective pullbacks in an appropriate category of algebras equipped with left and right coactions. This allows us to go beyond the category of comodule algebras when constructing examples of principal coactions. The aim of this talk is to show such an example by constructing a family of coalgebraic noncommutative deformations of the U(1)-principal bundle S7-> CP3 (Joint work with P. M. Hajac)
WEDNESDAY, 09 May, 2012 (IMPAN, room 106, Ist floor)
14:00 Simon Brain (Universite du Luxembourg)
THE DIFFERENTIAL AND TWISTOR GEOMETRYOF SELF-DUAL YANG-MILLS GAUGE FIELDS
THURSDAY, 10 May, 2012 (Warsaw, 74 Hoza street, 5th floor)
13:15 Elmar Wagner (Universidad Michoacana de San Nicolas de Hidalgo, Morelia, Mexico)
THE PULLBACK STRUCTURE OF THE STANDARD HOPF FIBRATION OF QUANTUM SU(2)
Participants
- Simon Brain (Universite du Luxembourg)
- Piotr M. Hajac (IMPAN/ University of Warsaw)
- Tomasz Maszczyk (University of Warsaw/IMPAN)
- Jan Rudnik (IMPAN)
- Elmar Wagner (Universidad Michoacana de San Nicolas de Hidalgo, Morelia, Mexico)