# Prof F Hirzebruch

Prof Hirzebruch has been director of the Max-Planck-Institut für Mathematik in Bonn over many of the years of Krzysztof's involvement with that institution. This message was read at the memorial service in Albuquerque.

The Max Planck Institute for Mathematics has lost a good friend due to a tragic accident. Krzysztof Galicki visited the Max Planck Institute frequently. From 1993 to 2006 he was our guest 13 times; in both 1997 and 2004 he stayed for a full year. He had applied for an additional research visit of six months in 2008, to begin on the 1st of January. Excellent letters of reference were received by prominent mathematicians, and his application was granted with enthusiasm. We are very sad that we have to miss him.

Krzysztof was a leading mathematician in differential geometry. His work on Einstein manifolds contains breakthroughs in the field. It is very difficult to construct Einstein manifolds of positive Ricci curvature. I am not an expert in differential geometry, but I have often studied exotic spheres. Therefore I especially like the result (in collaboration with C. P. Boyer, J. Kollár and E. Thomas) that all spheres in dimensions 4n+1, 7, 11, and 15 (that bound parallelizable manifolds) admit Sasakian-Einstein metrics. These were the first examples of Einstein metrics on exotic spheres. Krzysztof's work on the papers "Sasakian geometry, hypersurface singularities and Einstein metrics" (with C. P. Boyer) and "On Eta-Einstein Sasakian geometry" (with C. P. Boyer and P. Matzeu) was done to a large extent at the Max Planck Institute, where P. Matzeu visited him. For a Bonn mathematician it is good to see that Brieskorn's results on exotic spheres and hypersurface singularities play a role in Krzysztof's work and that there are many more connections to algebraic geometry and topology. Krzysztof was a mathematician with a broad outlook, who fitted very well into the Max Planck Institute. I could only indicate by way of example the wealth of his work. He liked it here, and we liked him. He wrote an impressive official report about his visit for the period January 1, 2004 to January 11, 2005. I quote: *"Finally, I have spent a very substantial amount of my time at the Institute writing a research monograph on Sasakian manifolds. This book has now almost 400 pages. We are writing it together with Charles Boyer (UNM) for the Oxford University Press. More than 50 % of my effort while visiting the MPI went into writing this book."* This book will appear soon. He did not live to enjoy this highlight of his mathematical career. At the end of his report, Krzysztof writes: *"Finally, I would like to thank the Institute for letting me spend my sabbatical year in Bonn. It was a truly wonderful year for me."*

The Max Planck Institute is very sad that such an experience cannot be repeated in the future. On behalf of the Max Planck Institute, in particular the managing director, Professor Werner Ballmann, I want to express our deeply felt sympathy to Krzysztof's wife, his parents in Poland, to his sister and her family in Australia, and to his colleagues and friends in the Department of Mathematics and Statistics at the University of New Mexico in Albuquerque.

Friedrich Hirzebruch

Bonn, October 31, 2007