Speaker: Isaac Goldbring, UC-Irvine
Title: On a problem of Fritz, Netzer, and Thom
Abstract: After being open for 50 years, the Connes Embedding Problem (CEP) in operator algebras was settled several years ago as a consequence of the quantum complexity result MIP*=RE. One equivalent formulation of the CEP is that the group $F_2\times F_2$ is residually finite-dimensional (RFD), where $F_2$ is the free group on 2 generators. In their 2012 paper, Fritz, Netzer, and Thom proved that any RFD group $G$ is such that the standard presentation of the universal group C*-algebra $C^*(G)$ is computable and thus raised the question as to whether or not the standard presentation of the universal group C*-algebra $C^*(F_2\times F_2)$ is computable, for a negative answer to this question would refute the CEP. While MIP*=RE settled the CEP, it failed to resolve the question of Fritz, Netzer, and Thom. In this talk, I will show that the standard presentation of the universal group C*-algebra $C^*(F_2\times F_2)$ is not computable, using an even more recent quantum complexity result known as MIP^{co}=coRE. Time permitting, I will discuss related results. The work presented in this talk is joint with Thomas Sinclair.
Talk will be presented virtually and can be viewed either in Carver 0401 or via https://iastate.zoom.us/j/93127761644