Abstract: How can two parties who are at a distance from one another carry out a fair coin flip? This problem has been an object of study for decades. Previous research has shown that coin flipping with positive bias (i.e., coin-flipping which permits a limited amount of cheating) is possible if the parties share a quantum information channel. Yet, proving quantum coin-flipping with bias tending to zero is mysteriously hard -- the only known protocol requires more than an exponential amount of communication.
This talk will be about a new result which untangles the mystery of why quantum coin-flipping is difficult. We will draw on some unexpected topics in mathematics (including the behavior of rational functions on complex numbers). Since this talk is aimed for a broad audience, the first half will be spent covering fundamental concepts and giving a detailed description of the central problem. The talk is based on https://arxiv.org/abs/1909.10103 .
Abstract: The recent paper "MIP*=RE" (arXiv:2001.04383) showed that, remarkably, quantum interactive proofs have essentially unlimited computational power. In the process, it refuted the longstanding Connes embedding conjecture. The goal of this group is to deconstruct some of the tools used in "MIP*=RE" (and its predecessors) and to study Connes' embedding problem. The first meeting will be an organizational meeting. All are welcome.
Abstract: I'll start with a quickie course on von Neumann algebras, for which a suitable reference might be Vaughan Jones' course notes, available at https://math.vanderbilt.edu/jonesvf/. Then I will state several equivalent forms of the Connes Embedding Problem, for which a good reference is arXiv:1003.2076.
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