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Over the past decade and a half, there has been a revolution in novel optical materials, with new directions continuously emerging. Some of the areas that we envisage this workshop encompassing include: (i) space-time microstructures (including foldable electromagnetic structures and manipulations of boundaries in time and space, where exciting phenomena have been observed); (ii) topological insulators, where topological constraints in the bulk lead to interesting surface effects and novel devices, arising through breaking space and/or time reversal symmetries and (iii) metasurfaces that can be tailored to achieve control of electromagnetic fields at interfaces, as well as meso-scale multi-physics problems coupling light with acoustic or elastic fields in structure media. The goals will be first to expose mathematicians to these developments. Then secondly, to develop a synthesis between mathematicians and other scientists to better understand these phenomena.