Mathematics Colloquia and Seminars

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We will consider the problem on complex crowns of Riemann symmetric spaces; it turns out that for such spaces there are canonical Stein neighbohoods on which can be holomorphicaly extent basic analytic objects on symmetric spaces(spherical functions, solutions of some invariat differential equations etc). The crowns also universaly appear in geometrical problems: parametrizations of cycles in flag domains, Matsuki duality etc. These remarkable domains continue to be en enigma in many points: sometimes they are homogeneous relative to a bigger group, sometimes they are inhomogeneous at all. A substantial progress was achieved in the last year.