Partition Functions and Models

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Elements of computational complexity

Covers classical and quantum computational complexity concepts and implications.

Scientific Machine Learning: Introduction to Spin Glass Models

Introduces Scientific Machine Learning, emphasizing its application in various scientific fields and the connection between machine learning and physics.

Phase Transitions in the Ising Model

Explores phase transitions in the Ising model, mean magnetization, susceptibility, critical exponents, and the universality of critical exponents.

Potts Model: Introduction

Introduces the Potts model, a generalization of the Ising model used in statistical mechanics to study phase transitions.

State Space Models: Expressivity of Transformers

Covers state space models and the expressivity of transformers in sequence copying tasks.

Complexity & Induction: Algorithms & Proofs

Covers worst-case complexity, algorithms, and proofs including mathematical induction and recursion.

Random Field Ising Model on Graphs

Explores the Random Field Ising Model on random graphs, discussing belief propagation updates and population dynamics.

Phase Transitions: Thermodynamics and Universality

Explores phase transitions in thermodynamics, emphasizing competition between phases controlled by temperature and the concept of universality.

Belief Propagation on Trees

Explores Belief Propagation on trees, discussing cavity marginals, message passing algorithms, and the computation of free entropy.

Phase Transitions

Explores phase transitions in two-dimensional systems and the critical behavior near transition points.