A landmark proof in computer science has also solved an important problem called the Connes embedding conjecture. Mathematicians are working to understand it. Imagine aliens landed on Earth and handed ...

In 1935, Albert Einstein, working with Boris Podolsky and Nathan Rosen, grappled with a possibility revealed by the new laws of quantum physics: that two particles could be entangled, or correlated, ...

Abstract For a compact quantum group 𝔾 of Kac type, we study the existence of a Haar trace-preserving embedding of the von Neumann algebra 𝐿∞(𝔾) into an ultrapower of the hyperfinite II₁-factor ...

You enter a cave. At the end of a dark corridor, you encounter a pair of sealed chambers. Inside each chamber is an all-knowing wizard. The prophecy says that with these oracles’ help, you can learn ...

This overview examines the field of sofic groups and operator algebras, an interdisciplinary domain interfacing group theory, functional analysis and mathematical physics. Sofic groups—distinguished ...

Quantum computers that use entangled quantum bits or qubits will be capable verify answers to an incredibly vast set of problems. The correspondence between entanglement and computing was previously ...