Abstract: 

Here is a natural question: suppose you have an object that behaves like an algebra, but all the rules (e.g. associativity) are only satisfied up to a small error. Is such an object close to an actual algebra that exactly satisfies all the rules? You will hear the answer in this talk. I'll also tell you about a specific application and motivation for this question, coming from quantum cellular automata. These are unitary quantum dynamics that only have local causal influence. They have a rich mathematical structure, but it is not known how fragile this structure is in general: what happens if the dynamics are not exactly unitary, or not exactly local? I'll explain how this is related to approximate algebras, and how we use this to show a robustness result in one spatial dimension. Based on arxiv:2603.08702, joint work with Daniel Ranard and Michael Walter.