The approach of Holowinsky and Soundararajan to the Quantum Unique Ergodicity conjecture (Emmanuel Kowalski, ETH, Zurich)

The lectures will sketch the recent approaches of Holowinsky
and Soundararajan towards the Quantum Unique Ergodicity conjecture,
based on analysis of shifted-convolution sums by sieve methods
(Holowinsky) and "weak-subconvexity" bounds for L-functions
(Soundararajan), and their successful combination in the case of
equidistribution for holomorphic cusp forms.