Proper Actions and Representation Theory. Part I. Properness criterion. Pat II. Discontinuous group, Weil's local rigidity, and deformation. Part III. Tempered Subgroups and tempered homogeneous spaces. Representations and Characters: Revisiting the Works of Harish-Chandra and André Weil — A satellite conference of the virtual ICM 2022 (organized by Hung Yean Loke, Tomasz Przebinda, Angela Pasquale, and Binyong Sun). The Institute for Mathematical Sciences, National University of Singapore, Singapore, 1-15 July 2022.

In the series of lecture, I plan to explain some recent topics on proper actions with emphasis on their relation to representation theory. I begin with some geometric problems of group actions including properness criterion for reductive homogeneous spaces. In turn, I introduce a ''quantification” of proper actions and bring geometric ideas to analytic representation theory such as temperedness criterion. Basic notion will be illustrated by examples. No special background knowledge will be required.

Tutorial Part I: 1 July 2022 (Friday), 11am–12noon

Tutorial Part II: 2 July 2022 (Saturday), 10.30–11.30am

Tutorial Part III: 4 July 2022 (Monday), 10.30–11.30am

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© Toshiyuki Kobayashi