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Creators/Authors contains: "Marzuola, Jeremy"

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  1. ; ; (, SIAM Journal on Scientific Computing)
    Free, publicly-accessible full text available April 30, 2026
  2. ; ; (, Journal de Mathématiques Pures et Appliquées)
    Free, publicly-accessible full text available April 1, 2026
  3. ; ; ; (, Journal of the London Mathematical Society)
    Abstract 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 partitions coincide with nodal partitions of Courant‐sharp Laplacian eigenfunctions. However, almost all minimal partitions are non‐bipartite. To study those, we define a modified Laplacian operator and prove that the nodal partitions of its Courant‐sharp eigenfunctions are minimal within a certain topological class of partitions. This yields new results in the non‐bipartite case and recovers the above known result in the bipartite case. Our approach is based on tools from algebraic topology, which we illustrate by a number of examples where the topological types of partitions are characterized by relative homology. 
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    Free, publicly-accessible full text available January 1, 2026
  4. ; ; (, The Journal of Geometric Analysis)
    Full Text Available 
  5. ; ; ; ; (, SIAM Journal on Matrix Analysis and Applications)
    Full Text Available 
  6. ; ; (, Transactions of the American Mathematical Society)
    We prove explicit asymptotics for the location of semiclassical scattering resonances in the setting of h h -dependent delta-function potentials on R \mathbb {R} . In the cases of two or three delta poles, we are able to show that resonances occur along specific lines of the form Im ⁡<#comment/> z ∼<#comment/> −<#comment/> γ<#comment/> h log ⁡<#comment/> ( 1 / h ) . \operatorname {Im}z \sim -\gamma h \log (1/h). More generally, we use the method of Newton polygons to show that resonances near the real axis may only occur along a finite collection of such lines, and we bound the possible number of values of the parameter γ<#comment/> . \gamma . We present numerical evidence of the existence of more and more possible values of γ<#comment/> \gamma for larger numbers of delta poles. 
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  7. ; (, Asymptotic Analysis)
    The aim of this paper is to provide uniform estimates for the eigenvalue spacing of one-dimensional semiclassical Schrödinger operators with singular potentials on the half-line. We introduce a new development of semiclassical measures related to families of Schrödinger operators that provides a means of establishing uniform non-concentration estimates within that class of operators. This dramatically simplifies analysis that would typically require detailed WKB expansions near the turning point, near the singular point and several gluing type results to connect various regions in the domain. 
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  8. ; (, Advances in Mathematics)
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  9. ; ; ; ; ; (, Journal of Nonlinear Science)
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  10. ; ; ; ; (, Numerische Mathematik)
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