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Award ID contains: 1900993

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  1. ; (, Mathematische Annalen)
    null (Ed.)
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  2. ; (, International Mathematics Research Notices)
    Abstract We show that real and imaginary parts of equivariant spherical harmonics on $${{\mathbb{S}}}^3$$ have almost surely a single nodal component. Moreover, if the degree of the spherical harmonic is $$N$$ and the equivariance degree is $$m$$, then the expected genus is proportional to $$m \left (\frac{N^2 - m^2}{2} + N\right ) $$. Hence, if $$\frac{m}{N}= c $$ for fixed $0 < c < 1$, then the genus has order $N^3$. 
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  3. ; (, Annales de l'Institut Fourier)
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