Geometric and harmonic analysis on homogeneous spaces and applications

Abstract

Lie group representation theory and harmonic analysis on Lie groups and on their homogeneous spaces have built up enormous stores of knowledge as a significant and indispensable area of mathematics since the end of the World War II when the research in these areas began. These areas are closely interrelated with various other mathematical fields such as number theory, algebraic geometry, differential geometry, operator algebra, partial differential equations and mathematical physics, and are still growing and developing. In these circumstances, Ali Baklouti and Takaaki Nomura got a plan to organize joint seminars. The first seminar took place on November 2009 in Kerkennah Islands. This seminar was focused upon analysis with the keyword harmonic analysis as a core in such vast spread of research areas within the framework of academic program under the cooperation of Ministry of Higher Education, Scientific Research and Technology in Tunisia (MHESRT) and Japan Society for the Promotion of Science (JSPS). Many researchers on the forefront in both countries, experts in the concerned research areas from different corners, brought together the newest research results and discussed further progress of their research. This was a boosting reason for Ali Baklouti and Takaaki Nomura to continue the collaboration through the organization of a second Tunisian–Japanese meeting which took place in Sousse (December 2011) and is planned to emphasis direction axes of research toward commutative harmonic analysis (Fourier analysis on Euclidean spaces), analysis on homogeneous spaces, uncertainty principles and geometric analysis and some of their applications such as stochastic analysis and spectral theory. This seminar is also combined with an exchange based on the reciprocity program between Faculty of Mathematics, Kyushu University and Faculty of Science, Sfax University. In this sense, we list up post-doctoral students at Kyushu University, young researchers who graduated from Kyushu University, and young researchers in Sfax University. We also include young mathematicians from other than the two universities in the research area of non-commutative harmonic analysis. Thus we keep our eyes also on possible future exchanges by these young mathematicians, and the seminar was not a single one-time exchange between senior researchers. It is not so often that mathematicians who just made their debut