Conference Agenda

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

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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

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