Monday 9am to noon: Morten S. Risager (University of Copenhagen) Title: Distributions of Manin’s iterated integrals Abstract: We discuss 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. In length one and two we determine the limiting distribution of these iterated integrals. Maybe surprisingly, even if we can compute all moments also in higher length we cannot determine a distribution for length three or higher except for in special cases. We discuss the proofs of these results which involves understanding a generalisation of Goldfeld Eisenstein series. This is joint work with Y. Petridis and with N. Matthes. ----------------------------------------------------------------------- Tuesday 9am to noon: Nikolaos Diamantis (University of Notthingham) Title: L-series associated with harmonic Maass forms and their values Abstract: We describe a new general definition of L-series associated with harmonic Maass forms and its functional equation. A converse theorem is formulated and potential applications are discussed. Special values of these L-series are studied and, as an application, an important cycle integral considered by Bruinier--Funke--Imamoglu and Ahlfes-Neumann--Schwagenscheidt is interpreted as a proper L-value. We further provide explicit expressions for special values of derivatives of our L-series which also have applications to standard cusp forms. The work presented is based on joint papers with M. Lee, W. Raji, L. Rolen and F. Stromberg. ----------------------------------------------------------------------- Wednesday 2pm to 5pm: Keshav Aggarwal (Rényi Institute) Title: Subconvexity bounds via delta methods Abstract: In the first part, I will present a few approaches involving the use of a delta method in order to obtain subconvexity bounds, with a focus on the works of Duke-Friedlander-Iwaniec and Munshi. In the second half, I will present a recent work done in collaboration with Munshi and Heung on bounding a short second moment average of a GL(3) L-function in order to achieve a subconvexity estimate. If time allows, I will try to draw comparisons between the various approaches. ----------------------------------------------------------------------- Thursday 2pm to 5pm: Anne-Maria Ernvall-Hytönen (University of Helsinki) 1st Title: General overview of exponential sums involving Fourier coefficients of cusp forms 1st Abstract: During this talk, I will give a general overview of different bounds that have been obtained for exponential sums involving Fourier coefficients of cusp forms. The focus will be in sums with linear parameters. 2nd Title: Higher moments of exponential sums involving Fourier coefficients of cusp forms 2nd Abstract: Typically short sums are extremely difficult to bound. We have good conjectures concerning how they behave, but we haven't been able to bound them. Therefore, it makes sense to look at the behaviour in average via looking at moments.