Develop discrete analogs of the AdS/CFT correspondence inspired from number theory, and understand their deep connection with the usual continuum formulation.
Study exact string dynamics in terms of algebraic evolution laws on discrete spacetimes.
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.