A workshop aimed at generating synergy between a fast-growing community of applied mathematicians interested in problems arising in “plasmonics” — currently one of the most exciting and vibrant fields in applied physics — and some of the leading physicists working in this field, including both theorists and experimentalists. 

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Background: There is currently a major scientific endeavour, carrying far-reaching ramifications to bio-sensing, imaging, medical treatment and defence applications, to devise methods to effectively manipulate light and light-matter interactions on subwavelength, nanometric, length scales. In particular, plasmonic techniques rely on the unique optical properties of metals in the visible spectrum and the ability to fabricate tailored metallic structures on the nanoscale. Over the last two decades, theoretical and experimental advancements in plasmonics have been influencing breakthroughs in other branches of nanophotonics and in the related field of metamaterials, with ideas crossing over to sound, elastic, seismic and water waves.

Plasmonics has also been attracting significant attention in applied mathematics, originally owing to a number of puzzling physical “paradoxes” and a surprising linkage found between the physical resonances of metallic nanostructures and classical spectral problems arising widely in mathematical analysis. The goal of this joint math-physics workshop is to present new developments in the field alongside novel exact, asymptotic and numerical methods and results. It’s an opportunity to generate new connections between physicists and applied mathematicians, exchange ideas and discover new potential collaborators with distinct toolkits. 

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Topics include:

1. New phenomena and physics in plasmonics and related topics, with emphasis on modelling challenges and open theoretical questions.

2. Transformation optics applied to plasmonics; novel asymptotic and numerical methods; modelling plasmonic structures with multiple-scale and singular geometries.

3. Spectral problems in nanophotonics: plasmonic eigenvalue problem, Neumann-Poincare operator and modal theory beyond the quasi-static regime. 

4. Paradoxes in plasmonics and metamaterials and their interpretation; singular effects of weak dissipation and material nonlocality.

5. Similar challenges in acoustic/elastic resonant wave-structure interactions.