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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Modular forms of half-integral weight on G_2

## Modular forms of half-integral weight on G_2Add to your list(s) Download to your calendar using vCal - Aaron Pollack (University of California, San Diego)
- Thursday 25 August 2022, 10:00-11:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact nobody. NC2W02 - Crossing the bridge: New connections in number theory and physics Classical holomorphic modular forms are number-theoretic objects that have been intensely studied. The split exceptional group G_2 does not support a theory of holomorphic modular forms, but it does possess so-called quaternionic modular forms. These are a special class of automorphic forms that appear to behave similarly to holomorphic modular forms. In the talk, I will describe a theory of modular forms of half-integral weight on G_2 and other exceptional groups. In particular, we prove the existence of a modular form of weight 1/2 on G_2 whose Fourier coefficients are related to the 2-torsion in the narrow class groups of totally real cubic fields. This is joint work with Spencer Leslie (Boston College). This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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