Lectures related to Turbulent State Symmetries

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 Theory

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

Renormalization & Scaling

Explores renormalization, scaling, critical points, exponents, and phase transitions in conformal field theory and quantum gravity.

Conformal Loop Ensembles: Connections to CFT

Explores the relationship between conformal loop ensembles and conformal field theory, focusing on the three-point nesting function and its mathematical derivation.

Conformal Field Theory: Generators and Commutation Relations

Covers the definition of generators of the conformal group and the application of Wick's theorem.

Conformal Transformations

Explores conformal transformations, scale invariance, and critical points in conformal symmetry.

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.

Neural Networks and Quantum Field Theory

Explores the connection between neural networks and quantum field theory, focusing on the correspondence between parameter and function spaces.

Unitarity Bounds: Operator Product Expansion

Covers unitarity bounds, operator product expansion, conformal blocks, and the conformal bootstrap in conformal field theory.

Conformal Field Theory Basics

Covers the basics of Conformal Field Theory, focusing on Large N CFTs and correlation functions.

Stochastic Integral: Isometry Continuity

Covers stochastic integrals, emphasizing isometry and continuity properties in martingales and different spaces.

Renormalization Group in Field Theory

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

Percolation: Bond Percolation

Covers bond percolation on a square lattice, discussing percolation phases, critical threshold, mean cluster size, and critical point scenarios.

Renormalization Group: Universal Critical Exponents

Explores the universal critical exponents of microscopic systems and the role of the renormalization group.

Turbulence and Symmetry

Introduces turbulence and symmetry in fluid dynamics, exploring the effects of Reynolds number on flow patterns.

Universality and Rotational Invariance in Isoradial Graphs

Covers universality and rotational invariance in isoradial graphs and their implications in statistical mechanics.

Stochastic Calculus: Itô's Formula

Covers Stochastic Calculus, focusing on Itô's Formula, Stochastic Differential Equations, martingale properties, and option pricing.

Stochastic Calculus: Brownian Motion

Explores stochastic processes in continuous time, emphasizing Brownian motion and related concepts.

Phase Transitions: Percolation in 2D Networks

Explores phase transitions through percolation in 2D networks.

Quadratic Variation: Martingales and Stochastic Integrals

Explores quadratic variation in martingales and stochastic integrals, emphasizing their properties and extensions.