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Oberwolfach Reports

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Volume 13, Issue 2, 2016, pp. 1259–1318
DOI: 10.4171/OWR/2016/23

Published online: 2017-02-07

Moduli spaces and Modular forms

Jan Hendrik Bruinier[1], Gerard van der Geer[2] and Valery Gritsenko[3]

(1) Technische Hochschule Darmstadt, Germany
(2) Amsterdam University, The Netherlands
(3) Université des Sciences et Technologies de Lille (USTL), France

The roots of both moduli spaces and modular forms go back to the theory of elliptic curves in the 19th century. Both topics have seen an enormous growth in the second half of the 20th century, but the interaction between the two remained limited. Recently there have been new developments that led to new points of contact between the two topics. One is the theory of K3 surfaces that is rapidly gaining a lot of new interest. Here the link with modular forms on orthogonal groups has led to progress on the Kodaira dimension of the moduli spaces of K3 surfaces. Another new development has been the use of moduli spaces of curves to gather new information about Siegel modular forms. The workshop intended to bring representatives from both the theory of moduli and the theory of modular forms together to further the interaction between the two topics as the time seemed ripe to do this.

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Bruinier Jan Hendrik, van der Geer Gerard, Gritsenko Valery: Moduli spaces and Modular forms. Oberwolfach Rep. 13 (2016), 1259-1318. doi: 10.4171/OWR/2016/23