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Explore mathematical insights about traveling waves in this 32-minute lecture by Vincent Calvez from the Centre national de la recherche scientifique (CNRS). Delivered on June 22nd, 2022, as part of the "Workshop on New Mathematical Theory to Understand the Effects of Evolution on Range Expansion" at the Fields Institute, delve into the fascinating world of mathematical modeling and its applications to evolutionary range expansion. Gain valuable knowledge about the mathematical concepts and theories underlying traveling waves, and discover how these principles can be applied to understand complex biological phenomena.