programme contributed to the status of IMPAN-Banach Center of an international
research and training centre. Due to it and other parallel international
programmes, mainly EC Centre of Excellence, it provided a critical mass of
scientists for some seminars to run and make joint research, attracting also
researchers from several Polish universities.
Some fellows made research on a very high level, in cooperation with and using advise of Polish researchers. Let me distinguish
- Juan J. Sanchez Alvarez-Dardet (Seville), who spent 12 months on the programme, wrote 2 papers joint with J. Zemanek, his scientist-in-charge in Warsaw.
He obtained results concerning power boundedness, Cesaro boundedness, and behaviour of the resolvents of linear operators, especially for the classical Volterra operator V. In particular, the powers of the operator I-V on Lp(0,1), 1≤ p≤∞, are bounded if and only if p=2. These results will be included in his PhD thesis.
- Gavin Band (Warwick), who spent here 6 months on this MCTS and also 2 months on the Centre of Excellence, finished writing here his PhD and prepared for publication an important paper "Identifying points of pseudo-Anosov homeomorphism" published in the high level international journal edited by IMPAN, Fundamenta Math. (2003),about possible embeddings of invariant sets in hyperbolic toral automorphisms, contributing to a solution to the conjecture that there are no non-trivial invariant submanifolds. This led him to study of Rouzy cocycles for interval exchange maps, which are of interest of leading mathematicians.
All fellows mention in their reports an excellent IMPAN mathematical library.