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Master class exploring the mathematical framework of Random Growth Loewner Evolution, a fundamental concept in mathematical physics that describes the evolution of random curves and interfaces. Delve into the theoretical foundations of Loewner evolution processes and their applications to random growth phenomena in statistical mechanics and probability theory. Examine the mathematical structures underlying stochastic Loewner evolution (SLE) and its connections to conformal field theory, critical percolation, and other models in mathematical physics. Investigate the geometric properties of random curves generated through Loewner evolution and understand how these processes model various physical systems exhibiting random growth patterns. Analyze the relationship between Loewner evolution and conformally invariant random curves, exploring the mathematical tools needed to study these complex stochastic processes. Study the applications of these concepts to understanding phase transitions, critical phenomena, and scaling limits in two-dimensional statistical mechanical models.
