Recorded 08 February 2022. Liran Rotem of Technion - Israel Institute of Technology presents "Spectral inequalities for rotation invariant measures" at IPAM's Calculus of Variations in Probability and Geometry Workshop. Abstract: We present new Brascamp-Lieb and Poincaré type inequalities, for measures which are log-concave with respect to rotation invariant measures. Geometric applications for proving Brunn-Minkowski type inequalities will also be given. In particular, we will resolve the (B) conjecture and the Gardner-Zvavitch conjecture for rotation invariant log-concave measures. Based on joint work with Dario Cordero-Erausquin.