Geometric Springer Proceedings in Mathematics & Statistics 3- Geometric and Harmonic Analysis on Homogeneous Spaces and Applications

Lie group representation theory and harmonic analysis on Lie groups and their homogeneousspaces form a significant area of mathematical research.



Lie group representation theory and harmonic analysis on Lie groups and their homogeneous spaces form a significant area of mathematical research. Interest in these areas began soon after World War II and has gained much strength since then. These areas are interrelated with various other mathematical fields such as number theory, algebraic geometry, differential geometry, operator algebra, partial differential equations, and mathematical physics. Keeping up with the fast development of this exciting area of research, Ali Baklouti (University of Sfax) and Takaaki Nomura (Kyushu University) launched a series of seminars on the topic. The main focus of these seminars was in the area of harmonic analysis, Lie theory, geometry and representation theory. Many experts from both countries have been involved in running this seminar and have contributed greatly to making seminars successful. This has been a major incentive for both Ali Baklouti and Hideyuki Ishi (Osaka University) to continue the organization of these meetings which aim at exploring topics such as commutative harmonic analysis (Fourier analysis on Euclidean spaces), analysis of homogeneous spaces, uncertainty principles, and geometric analysis and some of their interactions with operator algebras.