Turbulent State Symmetries

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

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

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

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

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

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

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

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

Explores phase transitions through percolation in 2D networks.

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