In the first pedagogical talk, I would give a quick introduction to the quantum field theory in condensed matter physics. I would firstly derive the path-integral representation of partition function for many-body systems. In such formulism, one could efficiently perform perturbation theory to calculate correlation functions using Feynman diagrams. Here, I will use the perturbative expansion of weakly interacting fermions as an example (may also cover the BCS problem depending on time.). I would also explain why we care about correlation functions in condensed matter physics.

In the second talk, I would use the path integral approach to study the SYK model. By analyzing the large-N structure, we will select the diagrams that contributes to the leading order of 1/N, which shows the conformal symmetry of the low-energy limit. Based on the result of two-point correlation function in the conformal limit , I will show the Lyapunov exponent is 2pi/beta. Finally I will discuss the derivation of the effective action of the system and talk about its relation to the AdS2 dilation gravity.