A Rigorous Study of the SYK Model

• Applicant: Dr. Chokri Manai
• Subject Area: Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 558731723

This project is dedicated to a mathematical investigation of the Sachdev-Ye-Kitaev (SYK) model. The SYK model is described by random Majorana interactions and has attracted a lot of attention in physics since its introduction about 10 years ago, mainly due to its relevance for solid state physics and gravitational physics. Mathematically, the SYK Hamiltonian is a sparse random matrix with a very special structure given by the Clifford algebra. Unfortunately, essential physical predictions about the ground state, the non-existence of a glass phase and relations to field theories are not well understood mathematically. My aim is to gain essential knowledge about the SYK model with an exact mathematical investigation. I want to apply and refine techniques from the fields of random matrices, statistical mechanics, operator theory and renormalisation groups.

• DFG Programme: Fellowship
• International Connection: USA
• Host: Professor Roland Bauerschmidt, Ph.D.