Ludwik DąbrowskiSISSA, Room 610
Phone: (+39) 0403787 422
Analytic and geometric methods in mathematical physics. The main topics of research:
- Schroedinger and Dirac operators with singular potentials.
- Global properties of spinor fields (spin structures) and gauge fields on (pseudo) Riemannian manifolds and their transformations under diffeomorphisms and other groups.
- Quantum groups (examples, representations and applications to exactly solvable models).
- Noncommutative geometry (construction of noncommutative manifolds, fibre bundles and connections, nontrivial solutions (e.g. solitons & instantons), metric and curvature in terms of the Dirac-type operators and spectral triples).
- PRIN 2008: "Spectral analysis and symmetries in quantum mechanics and noncommutative geometry", 2010-2011
- PRIN 2006-08: "Noncommutative geometry of quantum groups and their homogeneous spaces"
PRIN2004 Research Project: "Symmetries, singularities and integrability problems
in noncommutative geometry"
- INTAS Research Project 00-257 of the European Community
- PRIN2002 Research Project: "Singularities, Integrability, Symmetries"
- PRIN2000 Research Project "Singularities, Integrability, Symmetries"
- Friuli-Venezia Giulia Research Project 1999 "Noncommutative geometry: algebraic, analytical and probabilistic aspects and applications to mathematical physics"
- "Geometric Analysis", Research Training Network of the European Commission
Conferences and other events:
- Quantum Geometry and Matter 2013 April 2013, Trieste
- Trails in a noncommutative land, Trieste May 18-20, 2011
- Noncommutative geometry in representation theory and integrable systems, July 20-23, 2009 Trieste
- Workshop on Noncommutative Manifolds II, October 22-26, 2007 Trieste
- Sciences in Dialogue in the new Europe, June 27-29, 2007 Trieste
- Thematic Program on Noncommutative Geometry and Quantum Groups, June 20-30, 2006 Trieste
- Workshop on Noncommutative Manifolds, October 18-22, 2004 Trieste
- Spectral Problems for Schroedinger-type Operators, 11-14 March, 2003
- NCG2001 Workshop on Quantum Field Theory, Noncommutative Geometry and Quantum Probability