This program will focus on several aspects of the theory of automorphic forms with an emphasis on the relations among the internal structure of spaces of automorphic forms, the Langlands functoriality principle, automorphic L-functions, and questions in geometry, in particular, those regarding locally symmetric spaces. These are associated with arithmetic subgroups  of a given reductive algebraic group G defined over an algebraic number field.

Special attention is given to the theory of Eisenstein series and their ubiquitous role within the theory of automorphic forms. The fine structure of spaces of automorphic forms is essentially determined by the cuspidal support related to cuspidal automorphic representations of Levi subgroups of G and the Eisenstein series (or residues thereof) attached to them. In addition, degenerate Eisenstein series, that is, those series attached to automorphic representations which occur in the residual spectrum of Levi subgroups play an important role. In both cases, the study of the analytic properties, their relation with arithmetic, in the form of the theory of automorphic L-functions, is essential. Of course, the theory of local and global representations of G has to be used in these investigations.

As another aspect of the fine structure of spaces of automorphic forms, we also deal with extensions of automorphic representations. Already in cases of groups G with small k-rank, these extended automorphic forms present some important number-theoretical applications.

Hence, the proposed workshop would explore the possible implications and convergence of different lines of research towards the common goal of analytic behaviour of Eisenstein series. More precisely, the combination of the thorough understanding of the structure of spaces of automorphic forms, the inputs from the trace formula, as well as the use of certain structural advantages in certain cases, could lead to better understanding of the analytic properties of degenerate Eisenstein series, thus paving the way to several important applications in geometry and arithmetic. In particular, this broadened context offers a wealth of new accessible applications regarding the cohomology of arithmetic groups.

The workshop is additionally supported by the  Croatian Science Foundation.