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L-functions are among the key unifying themes of modern number theory: seemingly ubiquitous, one finds them naturally associated to number fields, automorphic forms, abelian varieties, Artin representations, and more.

Central analytic questions about L-functions include their moments, size, non-vanishing, distribution of zeros and have been key to expanding our understanding of the distribution of prime numbers, arithmetic statistics, equidistribution of special points and periods, Diophantine equations, random matrix theory, and quantum chaos. In turn, exciting progress on L-functions is being made using and often combining tools ranging from as far as exponential sums, oscillatory integrals, complex and p-adic analysis to spectral analysis, trace formulas, and algebraic geometry.

This summer school aims to introduce graduate students and young postdocs to a variety of approaches and techniques in the analytic theory of L-functions. The school will emphasize the thinking and intuition underlying various approaches, their use in practice and adaptability to a range of situations, and the organic unity of the subject.

Speakers:

Valentin Blomer (Universität Göttingen)
Philippe Michel (Ecole Polytechnique Fédérale de Lausanne)
Djordje Milićević (Bryn Mawr College)
Caroline Turnage-Butterbaugh (Duke University)
Matthew Young (Texas A&M University)