Coursera Flash Sale
40% Off Coursera Plus for 3 Months!
Grab it
Explore advanced concepts in planar statistical physics through this comprehensive master class that delves into the mathematical foundations and modern developments of two-dimensional statistical mechanical systems. Master the fundamentals of statistical mechanics, including ensemble theory, phase transitions, and critical phenomena in planar systems. Develop proficiency in Brownian motion and stochastic calculus, covering stochastic differential equations, Itô calculus, and their applications to statistical physics problems. Investigate geometric representations of lattice models, learning how to visualize and analyze complex statistical systems through geometric methods and combinatorial approaches. Study martingales and Markov processes extensively, understanding their theoretical foundations and practical applications in modeling random phenomena in statistical physics. Examine the conformal invariance properties of lattice models, exploring how scale invariance and conformal field theory connect discrete lattice systems to continuous field theories. Analyze various aspects of the Dimer and Ising models, two fundamental examples in statistical mechanics that exhibit rich mathematical structure and physical behavior. Discover the theory of random planar maps and their peeling processes, learning about the connections between discrete geometry, probability theory, and statistical physics. Gain insights into how these mathematical tools combine to provide a deep understanding of critical phenomena, phase transitions, and universal behavior in two-dimensional statistical systems.
