DescriptionWe all live in a world of phase transitions. Some we just observe (fog, morning dew), others we enforce (defrosting a freezer, cooking) or rely upon technologically (writing/playing ReWritable CD/DVDs). The common feature of these phenomena is an abrupt, usually non-smooth, change of the state of the system (one or more of its physical properties) which is caused by a small change of a single parameter (eg., temperature).Due to importance of phase transitions, many models were introduced aiming at better understanding of these phenomena, with examples covering a wide range of models in mathematics (such as random graphs, percolation), computer science (k-satisfiability) and science (Ising/Potts model, random-cluster model) to name just a few (some other examples and links can be found on this Wiki page). Despite complete solutions to various problems being rather difficult or even unknown, suprisingly enough simple counting arguments and probabilistic intuition at the 2H level lead to non-trivial results about the nature of the phase transition in various models. The aim of the project is to explore some of the mathematical methods used to study phase transitions. Prerequisites2H Probability and 4H Probability; 3H Stochastic Processes could be helpful.ResourcesDue to the abundance of choice and vast amount of available literature, concrete references shall be suggested on an individual basis.
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email: Ostap Hryniv