Fudan Logic Seminar 2026

March 30

Location: HGW2401

Speaker: Isaac Goldbring

Time: 16:00 - 17:30

On a problem of Fritz, Netzer, and Thom

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 $\mathrm{MIP}^{\mathrm{co}}=\mathrm{coRE}$. Time permitting, I will discuss related results. The work presented in this talk is joint with Thomas Sinclair. No prior knowledge of operator algebras or quantum complexity will be assumed.