I am a theoretical physicist sometimes drifted away into mathematics. One of my old ideas is how to encode quantum information and protect it from noise using “topological” many-body systems, for example, the Majorana chain. Now I am trying to find the mathematical structures that would describe all, or some well-defined class of, such topological quantum phases. I am also interested in the black hole information paradox and have recently found a simple Hamiltonian with many properties of a quantum black hole.