Automorphic forms and higher algebraic cycles

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• Aleksander Horawa (Oxford)
• Tuesday 30 January 2024, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Jef Laga.

We will explain a surprising relationship between the contributions to cohomology of automorphic forms and higher algebraic cycles. We will focus on two examples of automorphic forms of low weight on groups that have associated Shimura varieties: (1) Hilbert modular forms: we conjecture that the cohomology associated with weight one Hilbert modular forms is related to Stark units for an associated Artin representation. (2) Siegel modular forms: in recent work with Kartik Prasanna, we conjecture that the cohomology associated with weight two Siegel modular forms is related to higher algebraic cycles on a product of abelian surfaces over Q. We will discuss some evidence to support these conjectures.

This talk is part of the Number Theory Seminar series.

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