Large Sieve Inequalities for Families of Automorphic Forms

Explore the intricacies of large sieve inequalities for families of automorphic forms in this one-hour lecture by Matthew Young at the Hausdorff Center for Mathematics. Delve into the measurement of family understanding through these inequalities, examining optimal results for GL_1 and GL_2 families, including the classical large sieve and Deshouillers-Iwaniec's work. Investigate the current state of knowledge in higher rank families, with a focus on recent advancements in the GL_3 spectral large sieve. Cover key topics such as notation, family definitions, duality principle, Kuznetsov formula, and the contributions of Thorner and Zaman, while addressing challenges like truncation and exploring Heath-Brown's insights.

Intro
Notation
What is a family
Large sieve inequalities
G01 families
G02 families
The optimistic bound
The optimal bound
The duality principle
Kuznetsov formula
Thorner and Zaman
Rough idea
First issue
Truncation
Heath Brown