= Yaiza Canzani
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<Yaiza Canzani> works in <spectral geometry>, studying how the geometry of a space controls <eigenfunctions> and <eigenvalues> of its <Laplace operator>. Her research account includes bounds for eigenfunction concentration, averages over submanifolds and spectral counting remainders.https://canzani.web.unc.edu/research/[Publications and research topics]{ref}
Her <Analysis on Manifolds via the Laplacian by Yaiza Canzani> develops the geometry behind this spectral language. On a circle, for example, the modes $1$, $\cos(k\theta)$ and $\sin(k\theta)$ have nonnegative Laplace eigenvalues $0$ and $k^2$. Their oscillation scale grows with $k$, making the link between shape, frequency and eigenvalue tangible. On a general <Riemannian manifold>, the corresponding questions concern how waves concentrate and how geometry changes their allowed modes.<Analysis on Manifolds via the Laplacian by Yaiza Canzani>[Eigenfunction examples and variational characterization of the spectrum]{ref}
\Image[https://www.ias.edu/sites/default/files/styles/portrait/public/images/scholars/12757-1689182101.jpg.webp?itok=5L9CRJuH]
{title=Yaiza Canzani, portrait identified by the linked author, institutional or Commons source}
{height=240}
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