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This conference will cover the latest developments on the interface of noncommutative algebra, differential and algebraic geometry, and perspectives arising from physics. These connections have proven numerous in recent decades, leading to advances like the development of new and powerful knot invariants, new perspectives on enumerative geometry and string theory, and the introduction of cluster algebra and categorification techniques into a broad range of areas. These interactions mean that the speakers will span a number of areas of math, not often brought together in conference, while maintaining a clear theme. We are strongly committed to giving a diverse group of younger mathematicians an opportunity to speak on their results. We intend for the conference to enable fruitful interaction between researchers with different perspectives: from math and from physics, from algebra and from geometry. Having the conference at CIRM will bring together renowned specialists from around the world in these areas to interact with younger researchers, especially from France and more generally the EU and encourage informal interactions, leading to cross-fertilization. The conference will also mark the 60th birthday of the celebrated mathematician Nicolai Reshetikhin whose profound contributions revolutionized these subjects.