## *Birth of New Branching Problems*.
70th anniversary lecture (featured invited talk), MSJ Autumn Meeting 2016. Kansai University, Japan, 15-18 September
2016.

2016年度秋季総合分科会,
日本数学会70周年記念講演（企画特別講演）

The local to global study of geometries was a major trend of 20th
century, with remarkable developments achieved particularly in
Riemannian geometry. In contrast, surprising little was known 30 years
ago about global properties of locally homogeneous spaces with
indefinite-metric, which led us to the theory of discontinuous groups
beyond the Riemannian setting.
Concerning linear actions (representation theory), one of fundamental
problems is to understand how things are built from smallest objects
(irreducible decomposition). Branching problems are typical case, but
were supposed to be out of control for reductive Lie groups.
Breakthrough ideas for branching problems in representation theory
emerged partially from the study of discontinuous groups beyond
Riemannian setting, and conversely, they have opened new research such
as global analysis of indefinite-Riemannian locally symmetric spaces (e.
g. anti-de Sitter manifolds).

Based on the developments over the last two decades, we present a
program on branching problems, from the general theory to concrete
construction of symmetry breaking operators.

© Toshiyuki Kobayashi