I will talk on Cannes's Embedding Conjecture, which is considered as one of the most important open problems in the field of operator algebras. It asserts that every finite von Neumann algebra is approximable by matrix algebras in suitable sense. It turns out, most notably by Kirchberg, that Cannes's Embedding Conjecture is equivalent to surprisingly
many other important conjectures which touches almost all the subfields of operator algebras and also to other branches of mathematics such as quantum information theory and noncommutative real algebraic geometry.
