T. Kobayashi, Conjectures on reductive homogeneous spaces, Mathematics Going Forward: Collected Mathematical Brushstrokes, J.-M. Morel and B. Teissier (eds.), Lecture Notes in Mathematics, vol. 2313, pp. 217-231, Springer, 2023, DOI: 10.1007/978-3-031-12244-6_17. Available also at arXiv: 2204.08854..

We address some conjectures and open problems in 'analysis of symmetries' which include the study of non-commutative harmonic analysis and discontinuous groups for reductive homogeneous spaces beyond the classical framework:

(1) discrete series for non-symmetric homogeneous spaces G/H;
(2) discontinuous group Γ for G/H beyond the Riemannian setting;
(3) analysis on pseudo-Riemannian locally homogeneous spaces.

DOI | arXiv | preprint version(pdf) ]

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