| Abstract: |
| A small metallic particle exposed to electromagnetic radiation with wavelength much larger than its size exhibits shape-dependent resonant frequencies, a phenomenon known as surface plasmon resonance. In the quasi-static regime, this effect is described by a Laplace transmission problem, which can be reformulated as an eigenvalue problem for the Neumann--Poincar\`e (NP) operator, a boundary integral operator associated with the harmonic double-layer potential.
In this talk, based on recent work (arXiv:2504.00696), I will discuss how the NP eigenvalues depend on smooth deformations of the domain. In particular, we will see that simple eigenvalues, as well as symmetric functions of multiple eigenvalues, depend real-analytically on the shape. We will also describe explicit formulas for their first shape derivatives and discuss some further consequences of these results. |
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