This volume contains the proceedings of the conference "Casimir Force, Casimir Operators and the Riemann Hypothesis – Mathematics for Innovation in Industry and Science" held in November 2009 in Fukuoka (Japan). The motive for the conference was the celebration of the 100th birthday of Casimir and the 150th birthday of the Riemann hypothesis.

The conference focused on the following topics:



Casimir operators in harmonic analysis and representation theory
Number theory, in particular zeta functions and cryptography
Casimir force in physics and its relation with nano-science
Mathematical biology
Importance of mathematics for innovation in industry

The latter topic was inspired both by the call for innovation in industry worldwide and by the fact that Casimir, who was the director of Philips research for a long time in his career, had an outspoken opinion on the importance of fundamental science for industry.

These proceedings are of interest both to research mathematicians and to those interested in the role science, and in particular mathematics, can play in innovation in industry.

Contributions by: Mihai Ciucu, Alain Connes, Caterina Consani, Christopher Deninger, Keisuke Hakuta, Shai M. J. Haran, Gert Heckman, Roger Howe, Minoru Itoh, Kazufumi Kimoto, Shin-Ya Koyama, Nobushige Kurokawa, Eduard Looijenga, Dan Lu, Hiroyuki Ochiai, Jinsung Park, Samuel J. Patterson, Michael Pevzner, Hisayoshi Sato, Martin F. H. Schuurmans, Binyong Sun, Tsuyoshi Takagi, Eng Chye Tan, Evgeny A. Verbitskiy, Chen-Bo Zhu