Europe/Lisbon — Online

Ingmar Saberi, Ludwig-Maximilians University Munich
Networks of perfect tensors via symplectic geometry over finite fields

There has been much excitement in the recent literature about the idea that tensor network models, which construct states whose entanglement properties mimic those of CFT vacua, correspond geometrically to a bulk space one dimension higher. Such discrete models of holography tend to miss at least two interesting features of the continuum AdS/CFT correspondence: there, an essential ingredient is the group of isometries, which acts via conformal transformations of the boundary. Furthermore, the local data in tensor networks (a choice of a finite-rank tensor, which is taken to be "perfect" in one interesting class of models) is not obviously related to any dynamics that resemble field theory. I'll give a rather biased outsider's perspective on approaches to both of these issues, taking inspiration in each case from algebraic geometry.