The holomorphic Quantum Unique Ergodicity (QUE) is a phenomenon where the probability measures associated to holomorphic newforms tend weakly to a unique uniform distribution, as the product of their weight and level tends to infinity. The holomorphic QUE of level 1 was proved by Soundararajan and Holowinsky. Notably, each of these methods encounters rare yet non-overlapping exceptions, which, when combined, yield a complete proof. In this talk, I will discuss the key ideas in Soundararajan’s and Holowinsky’s methods and briefly present the case when the level is arbitrary. If time allows, I will also talk about some new results that I proved as part of my project on this topic.

Talk by Ploy Wattanawanichkul.