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This workshop is part of a series of mathematical research activities organized by the Department of Mathematical Sciences at the University of Bath and Mexican mathematicians based in UNAM and CIMAT (BUC). The woorkshop will combine two kinds of activity: research talks in the morning and collaboration sessions in the afternoon. The morning talks will be given by analysts from Bath, IIMAS–UNAM, and CIMAT who will highlight the current research interests within the three institutions in the areas of differential equations, operator theory, and their applications to mathematical physics, materials science, wave propagation in continuum mechanics and electromagnetism. The material of the talks will be used as a basis for making an advance on the interfaces between the subjects touched upon.