Focused Workshop on Automorphic Forms

The purpose of this focused workshop is to discuss some recent developments in the theory of automorphic forms in a friendly and relaxed setting.

Report:

The purpose of the focused workshop was to learn about recent new techniques in a friendly and relaxed setting. There were four double lectures by four distinguished colleagues.

Morten S. Risager (University of Copenhagen) discussed the definition and properties of Manin’s iterated integrals of a given length, including how these generalise modular symbols and certain aspects of the theory of multiple zeta-values.

Nikolaos Diamantis (University of Notthingham) described a new general definition of L-series associated with harmonic Maass forms and its functional equation. A converse theorem was formulated and potential applications were discussed.

Keshav Aggarwal (Rényi Institute) presented a few approaches involving the use of a delta method in order to obtain subconvexity bounds. He also presented his recent work on bounding a short second moment average of a GL(3) L-function in order to achieve a subconvexity estimate.

Anne-Maria Ernvall-Hytönen (University of Helsinki) gave a general overview of different bounds that have been obtained or conjectured for exponential sums involving Fourier coefficients of cusp forms.