p-adics

Develop discrete analogs of the AdS/CFT correspondence inspired from number theory, and understand their deep connection with the usual continuum formulation.

Investigate quantum field theory on p-adic spaces and its relation to QFT on continuous spacetime. The simplest constructions of QFT on p-adic spaces are nonlocal, have an inherently hiearchical nature, and enjoy various powerful properties such as a non-renormalization theorem.

Explore the deep connections between quantum error-correcting codes and gravity in the framework of the AdS/CFT correspondence.