Subhajit Jana, Queen Mary University of London
We will talk about the local L2 bounds of the Eisenstein series on the general reductive groups. First, we will discuss how the Maass—Selberg relations, when used to understand the L2 norm of an Eisenstein series, yields a complicated combinatorial problem. Second, we will discuss how the ideas from Finis–Lapid–Muller’s fine spectral expansion of the Arthur–Selberg trace formula may be used to bypass the problem. Finally, we will talk about how such bounds can be used to conclude the proof of Sarnak’s Optimal Lifting Conjecture after Assing—Blomer. These are joint works with Amitay Kamber.