Lectures related to Universality and Rotational Invariance in Isoradial Graphs

FK-Percolation and the Six-Vertex Model: Critical Phenomena

Covers the transition from the six-vertex model to FK-percolation, focusing on critical phenomena and phase transitions in two-dimensional systems.

Percolation: Random Graph Models

Covers percolation theory and random graph models, exploring connectivity thresholds and critical power for wireless networks.

Stochastic Block Model

Covers the Stochastic Block Model and its application in community detection, exploring its mathematical formulation and challenges.

Graph Theory: Girth and Independence

Covers girth, independence, probability, union bound, sets, and hypergraph recoloring.

Independence and Covariance

Explores independence and covariance between random variables, discussing their implications and calculation methods.

Graphical Models: Probability Distributions and Factor Graphs

Covers graphical models for probability distributions and factor graphs representation.

Graphical Models: Representing Probabilistic Distributions

Covers graphical models for probabilistic distributions using graphs, nodes, and edges.

Renormalization Group in Field Theory

Explores the Renormalization Group in field theory, discussing scaling functions, critical exponents, and Gaussian fixed points.

Probabilistic method and its applications

Introduces the probabilistic method to prove existence results in graph theory.

Percolation Theory

Covers percolation theory, absorbed polymers, giant molecules, phase transition, scaling assumptions, and universal behavior in percolation models.

Correlation Functions in Loop Models: Structural Assumptions

Covers correlation functions in loop models and the role of degenerate fields in conformal field theory.

Epidemics and Bootstrap Percolation in Square Lattice

Explores epidemics spread models and Bootstrap Percolation in square lattice networks, focusing on the Kolmogorov equation and probability generating functions.

Dependence and Correlation

Explores dependence, correlation, and conditional expectations in probability and statistics, highlighting their significance and limitations.

Spherical Symmetry in Statistical Mechanics

Explores spherical symmetry in statistical mechanics and its role in phase transitions.

Dense Graphs: From Theory to Applications

Explores the transition from sparse to dense graphs and their real-world applications.

Central Limit Theorem: Properties and Applications

Explores the Central Limit Theorem, covariance, correlation, joint random variables, quantiles, and the law of large numbers.

Quantum Length of SLE: Natural Parameterization and Properties

Covers the quantum length of SLE and its natural parameterization, exploring key properties and relationships with random planar maps.

Fixed Points in Graph Theory

Focuses on fixed points in graph theory and their implications in algorithms and analysis.

Variance and Covariance: Properties and Examples

Explores variance, covariance, and practical applications in statistics and probability.

Probability and Statistics

Covers probability, statistics, independence, covariance, correlation, and random variables.