Spectral Independence in High-Dimensional Expanders and Applications to the Hardcore Model

This course covers the concept of spectral independence in high-dimensional expanders and its application to the Hardcore Model. The learning outcomes include understanding the Glauber Dynamics, the importance of the Hardcore Model, a complexity phase transition, and future research directions. The course teaches skills in analyzing spectral independence, applying it to the Hardcore Model, and outlining strategies for related problems. The teaching method involves lectures and theoretical discussions. The intended audience for this course includes researchers, academics, and students interested in theoretical computer science and probabilistic graphical models.