The National Science Foundation (NSF) awarded a $117,660 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program to Trustees of Dartmouth College for the project "Distribution of the Hodge and the Tate Locus - Geometry and Arithmetic." The project aims to study the distribution of the exceptional Hodge locus in variations of Hodge structures and the arithmetic counterpart, the Tate locus, using tools from Arakelov intersection theory, ergodic theory, Hodge theory, the Ax-Schanuel theorem for Shimura varieties, and Diophantine geometry. The research is expected to lead to advances in understanding the modularity behavior of special cycles in moduli spaces of K3 surfaces and orthogonal Shimura varieties. The project will also involve graduate student participation and the organization of a conference on recent developments in Hodge theory. No subcontracts are planned under this award, which has an ultimate completion date of June 30, 2026.
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