The main focus of the school will be the mathematics around the L-functions and modular forms database (LMFDB). It will introduce the students to the main ideas and philosophies around modularity theorems, which connect algebraic curves and abelian varieties on one side with modular forms and L-functions on the other. Theoretically, such ideas are part of the Langlands program; the LMFDB can be seen as a way to make this program accessible and concrete by means of a huge treasure trove of examples. A main series of plenary lectures will introduce the students to L-functions, modular forms, elliptic curves, and their relations. It will also show how these interconnections generalize to broader contexts, such as those of curves of small genus and abelian varieties.

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