Y. Canzani

activity

20102026

most citedScaling Limit for the Kernel of the Spectral Projector and Remainder Estimates in the Pointwise Weyl Law

24 citations · 94 across the 24 of their papers we have counts for

collaborators

32 papers

math.AP2026

Eigenfunction asymptotics and nodal domain estimates for dumbbell domains

Thomas Beck, Yaiza Canzani, Jeremy L. Marzuola

We study the nodal structure of Neumann eigenfunctions on planar dumbbell domains as the width of the neck joining two fixed end domains tends to zero. Under simplicity and non-deg…

math-ph2025

Shell energies derived from three-dimensional isotropic strain-gradient elasticity

C. Balitactac, Y. Canzani, R. S. Hallyburton +2

We derive a class of two-dimensional shell energies for thin elastic bodies exhibiting small-length scale effects modeled via strain-gradient elasticity. Building on the final auth…

math.NA2025

On non-local exchange and scattering operators in domain decomposition methods

Thomas Beck, Yaiza Canzani, Jeremy L. Marzuola

We study non-local exchange and scattering operators arising in domain decomposition algorithms for solving elliptic problems on domains in $R^{2}$ . Motivated by recent form…

math.AP2024

Stability of spectral partitions with corners

Gregory Berkolaiko, Yaiza Canzani, Graham Cox +2

A spectral minimal partition of a manifold is a decomposition into disjoint open sets that minimizes a spectral energy functional. While it is known that bipartite minimal partitio…

math.AP2024

Homology of spectral minimal partitions

Gregory Berkolaiko, Yaiza Canzani, Graham Cox +1

A spectral minimal partition of a manifold is its decomposition into disjoint open sets that minimizes a spectral energy functional. It is known that bipartite spectral minimal par…

math.SP2023★ 1 cited

Uniform upper bounds on Courant sharp Neumann eigenvalues of chain domains

Thomas Beck, Yaiza Canzani, Jeremy L. Marzuola

We obtain upper bounds on the number of nodal domains of Laplace eigenfunctions on chain domains with Neumann boundary conditions. The chain domains consist of a family of planar d…

math.AP2022

Asymptotics for the spectral function on Zoll manifolds

Yaiza Canzani, Jeffrey Galkowski, Blake Keeler

Let $(M, g)$ be a Zoll manifold, i.e., a smooth, compact, Riemannian manifold without boundary all of whose geodesics are closed with a minimal common period $T$ . The positive defin…

math.AP2022

Lower bounds for eigenfunction restrictions in lacunary regions

Yaiza Canzani, John A. Toth

Let $(M, g)$ be a compact, smooth Riemannian manifold and ${u_{h}}$ be a sequence of $L^{2}$ -normalized Laplace eigenfunctions that has a localized defect measure $μ$ in the sense tha…

math.DS2022

Logarithmic improvements in the Weyl law and exponential bounds on the number of closed geodesics are predominant

Yaiza Canzani, Jeffrey Galkowski

Let $M$ be a smooth compact manifold of dimension $d$ without boundary. We introduce the concept of predominance for Riemannian metrics on $M$ , a notion analogous to full Lebesgue…

math.AP2021★ 4 cited

Quantitative bounds on Impedance-to-Impedance operators with applications to fast direct solvers for PDEs

Thomas Beck, Yaiza Canzani, Jeremy L. Marzuola

We prove quantitative norm bounds for a family of operators involving impedance boundary conditions on convex, polygonal domains. A robust numerical construction of Helmholtz scatt…

math.AP2020

Weyl remainders: an application of geodesic beams

Yaiza Canzani, Jeffrey Galkowski

We obtain new quantitative estimates on Weyl Law remainders under dynamical assumptions on the geodesic flow. On a smooth compact Riemannian manifold $(M, g)$ of dimension $n$ , let…

math-ph2020★ 7 cited

A local test for global extrema in the dispersion relation of a periodic graph

Gregory Berkolaiko, Yaiza Canzani, Graham Cox +1

We consider a family of periodic tight-binding models (combinatorial graphs) that have the minimal number of links between copies of the fundamental domain. For this family we esta…

math.AP2020★ 8 cited

Growth of high $L^{p}$ norms for eigenfunctions: an application of geodesic beams

Yaiza Canzani, Jeffrey Galkowski

This work concerns $L^{p}$ norms of high energy Laplace eigenfunctions, $(- Δ_{g} - λ^{2}) ϕ_{λ} = 0$ , $∥ ϕ_{λ} ∥_{L^{2}} = 1$ . In 1988, Sogge gave optimal estimates on the growth of $∥ ϕ_{λ} ∥_{L^{p}}$ f…

math.AP2019

Nodal line estimates for the second Dirichlet eigenfunction

Thomas Beck, Yaiza Canzani, Jeremy L. Marzuola

We study the nodal curves of low energy Dirichlet eigenfunctions in generalized curvilinear quadrilaterals. The techniques can be seen as a generalization of the tools developed by…

math.AP2019

Eigenfunction concentration via geodesic beams

Yaiza Canzani, Jeffrey Galkowski

In this article we develop new techniques for studying concentration of Laplace eigenfunctions $ϕ_{λ}$ as their frequency, $λ$ , grows. The method consists of controlling $ϕ_{λ} (x)$ by…

math.AP2018★ 1 cited

Improvements for eigenfunction averages: An application of geodesic beams

Yaiza Canzani, Jeffrey Galkowski

Let $(M, g)$ be a smooth, compact Riemannian manifold and ${ϕ_{λ}}$ an $L^{2}$ -normalized sequence of Laplace eigenfunctions, $- Δ_{g} ϕ_{λ} = λ^{2} ϕ_{λ}$ . Given a smooth submanifold $H \subset…

math.AP2017★ 11 cited

On the growth of eigenfunction averages: microlocalization and geometry

Yaiza Canzani, Jeffrey Galkowski

Let $(M, g)$ be a smooth, compact Riemannian manifold and ${ϕ_{h}}$ an $L^{2}$ -normalized sequence of Laplace eigenfunctions, $- h^{2} Δ_{g} ϕ_{h} = ϕ_{h}$ . Given a smooth submanifold $H \subset M…

math.AP2017★ 16 cited

Averages of eigenfunctions over hypersurfaces

Yaiza Canzani, Jeffrey Galkowski, John A. Toth

Let $(M, g)$ be a compact, smooth, Riemannian manifold and ${ϕ_{h}}$ an $L^{2}$ -normalized sequence of Laplace eigenfunctions with defect measure $μ$ . Let $H$ be a smooth hypersurfa…

math.AP2016

Topology and nesting of the zero set components of monochromatic random waves

Yaiza Canzani, Peter Sarnak

This paper is dedicated to the study of the topologies and nesting configurations of the components of the zero set of monochromatic random waves. We prove that the probability of…

math.PR2016

Local Universality for Zeros and Critical Points of Monochromatic Random Waves

Yaiza Canzani, Boris Hanin

This paper concerns the asymptotic behavior of zeros and critical points for monochromatic random waves $ϕ_{λ}$ of frequency $λ$ on a compact, smooth, Riemannian manifold $(M, g)$ as…

math.AP2016★ 1 cited

C-infinity Scaling Asymptotics for the Spectral Function of the Laplacian

Yaiza Canzani, Boris Hanin

This article concerns new off-diagonal estimates on the remainder and its derivatives in the pointwise Weyl law on a compact n-dimensional Riemannian manifold. As an application, w…

math.AP2015

Nodal sets of Schrödinger eigenfunctions in forbidden regions

Yaiza Canzani, John Toth

This note concerns the nodal sets of eigenfunctions of semiclassical Schrödinger operators acting on compact, smooth, Riemannian manifolds, with no boundary. We prove that if H is…

math-ph2014★ 11 cited

On the topology of the zero sets of monochromatic random waves

Yaiza Canzani, Peter Sarnak

This note concerns the topology of the connected components of the zero sets of monochromatic random waves on compact Riemannian manifolds without boundary. In [SW] it is shown tha…

math.SP2014★ 24 cited

Scaling Limit for the Kernel of the Spectral Projector and Remainder Estimates in the Pointwise Weyl Law

Yaiza Canzani, Boris Hanin

Let (M, g) be a compact smooth Riemannian manifold. We obtain new off-diagonal estimates as λ tend to infinity for the remainder in the pointwise Weyl Law for the kernel of the spe…

Eigenfunction asymptotics and nodal domain estimates for dumbbell domains

Shell energies derived from three-dimensional isotropic strain-gradient elasticity

On non-local exchange and scattering operators in domain decomposition methods

Stability of spectral partitions with corners

Homology of spectral minimal partitions

Uniform upper bounds on Courant sharp Neumann eigenvalues of chain domains

Asymptotics for the spectral function on Zoll manifolds

Lower bounds for eigenfunction restrictions in lacunary regions

Logarithmic improvements in the Weyl law and exponential bounds on the number of closed geodesics are predominant

Quantitative bounds on Impedance-to-Impedance operators with applications to fast direct solvers for PDEs

Weyl remainders: an application of geodesic beams

A local test for global extrema in the dispersion relation of a periodic graph

Growth of high Lp norms for eigenfunctions: an application of geodesic beams

Nodal line estimates for the second Dirichlet eigenfunction

Eigenfunction concentration via geodesic beams

Improvements for eigenfunction averages: An application of geodesic beams

On the growth of eigenfunction averages: microlocalization and geometry

Averages of eigenfunctions over hypersurfaces

Topology and nesting of the zero set components of monochromatic random waves

Local Universality for Zeros and Critical Points of Monochromatic Random Waves

C-infinity Scaling Asymptotics for the Spectral Function of the Laplacian

Nodal sets of Schrödinger eigenfunctions in forbidden regions

On the topology of the zero sets of monochromatic random waves

Scaling Limit for the Kernel of the Spectral Projector and Remainder Estimates in the Pointwise Weyl Law

Growth of high $L^{p}$ norms for eigenfunctions: an application of geodesic beams