Holomorphic Quantum Unique Ergodicity – Ploy Wattanawanichkul

Quantum Unique Ergodicity (QUE) is a phenomenon where the probability density associated to any density one set of Eigenfunctions of the Laplacian on specific Riemannian manifolds tends weakly to the same uniform distribution, as their eigenvalues tend towards infinity. My focus lies in the analogous context, where we consider the mass equidistribution of holomorphic newforms when taking their weights to infinity. The resolution for the newforms of level 1 case combines two distinct approaches 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 aim to introduce a general background on the problem and provide some key ideas of the two methods.

Talk by Ploy (Nawapan) Wattanawanichkul.

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