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Session

NT1: Number Theory Time: Monday, 07/Sept/2026: 1:30pm - 3:30pm Session Chair: Ozlem Imamoglu Session Chair: Anna-Maria Pippich Location: Audimax A600

Presentations

Sums of Hecke eigenvalues along polynomials and base change Katharine Woo Stanford University We study sums of absolute values of Hecke eigenvalues of $\textrm{GL}(2)$ representations that are tempered at all finite places. We show that these sums exhibit logarithmic savings over the trivial bound if and only if the representation is cuspidal. Further, we connect the problem of studying the sums of Hecke eigenvalues along polynomial values to the base change problem for $\textrm{GL}(2).$ Discussion - - Arithmetic intersections of line bundles with singular metrics Jürg Kramer Humboldt-Universität zu Berlin, Germany In our talk, we will present an extension of arithmetic intersection theory of adelic divisors on quasi-projective varieties introduced by Yuan--Zhang to the case where these divisors are not necessarily arithmetically nef. The key tool to realize this extension is the concept of relative finite energy established by T. Darvas et al.. In particular, our theory will allow to compute heights on mixed Shimura varieties, e.g., the arithmetic self-intersection number of the line bundle of Siegel--Jacobi forms on the universal abelian variety. This is joint work with José Burgos Gil. Discussion - -