The rigidity properties of higher rank diagonalizable actionsis a
major theme in homogenous dynamics, with origins in work of Cassels and
Swinnerton-Dyer in the 1950s and Furstenberg. We survey both results and
conjectures regarding such actions, with emphasize on the applications of these results towards understanding the distribution of integerpoints on varieties, quantum unique ergodicity, and Diophantine approximations.

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https://huji.zoom.us/j/87131022302?pwd=SnRwSFRDNXZ4QVFKSnJ1Wit2cjZtdz09