Course 1: Bulbul Chakrabarty

Lecture 1 - Overview
Lecture 2 - The Statistical Physics of Athermal Materials
                - Lecture 2
Lecture 3 - Isostatic argument for frictional particles
Lecture 4 - Elasticity from gueage theory


Course 2: Leticia Cugliandolo

Lecture 1 - Out of equilibrium dynamics of complex systems
Lecture 2 - Coarsening
Lecture 3 - References and answers to questions
Lecture 4 - Disorder


Course 3: Manas Kulkarni

Course structure and reading material


Course 4: Gregory Schehr

Course outline

I) (Lecture 1 and 2) Introduction to Random Matrix Theory (RMT) 
Lecture 1
Lecture 2

    1) General overview of applications of RMT: from Wigner to Kardar-Parisi-Zhang (KPZ) equation
    2) Ensembles of RMT
        2.1) Wigner matrices
        2.2) Rotationally inv. ens. of RMT 
        2.3) Joint law of eingenvalues for Gaussian Orthogonal and Unitary Ensembles (GOE/GUE)
    3) Coulomb gas approach 
        3.1) Physical interpretation of the joint PDF of the eigenvalues and the log-gas
        3.2) Discuss the Wigner semi-circle and its universality                         

    4) Local statistics
        4.1) Bulk (Wigner surmise)
        4.2) Edge (Tracy-Widom fluctuations and applications to KPZ)
II) (Lecture 3-Lecture 4): Fermions and connections to RMT -- 1 lecture + 1/3 lecture
Lecture 3
Lecture 4

     1) Harmonic potential without interactions at T=0 and the GUE

     2) Finite Temperature and connections to KPZ     

     3) Interacting fermions and matrix models

III) (Lecture 4-5) Non-intersecting paths and Dyson’s Brownian motion
Lecture 5

    1) Non intersecting Brownian motions and non-interacting fermions

    2) Connection to RMT 

    3) Dyson’s Brownian motion 
    4) More recent developments


Course 5: Arnab Sen

Introduction to some basic notions of thermalization under unitary dynamics in many-body quantum systems, eigenstate thermalization hypothesis and its violations 

  • Integrable models (S=1/2 transverse field Ising model in one dimension, calculation of entanglement entropy, demonstration of volume law entanglement for high-energy states, locality of conservation laws) 
  • Quantum many-body scars in translationally invariant systems (PXP model etc, anomalous dynamics from special initial conditions, connection to lattice gauge theory) 
  • Many-body localization and the l-bit picture (emergent integrability, non-ergodic phase of matter) 
  • Periodically driven (Floquet) time crystals in many-body localized systems and breaking of discrete time-translation symmetry. Prethermal versions of time crystals without disorder 

Background: Earlier lectures by Arul and Subroto in the Bangalore Stat. Phys. Schools.

Course 6: Hugo Touchette

Course structure