Stochastic Partial Differential Equations and Interacting particle systems

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In broad terms, as far as the subject of my PhD is concerned, it involves an interplay of analysis, stochastic analysis and calculus of variations.To be precise, the project will be mainly focused on the topic of Stochastic Partial Differential Equations (SPDEs). Field of Stochastic Partial Differential Equations is quite new, the necessity of studying Stochastic Partial Differential Equations has been strongly motivated by applications. For example, in physics from problems such as wave propagation in random media and turbulence. Significant stimuli have also come from biology and neurobiology, in particular from population genetics.Recent research efforts conducted in 2014 led to major discoveries in the field of Stochastic Partial Differential Equations, and this has opened to a wide range of new problems to be studied.The analysis of Stochastic Partial Differential Equations is also related to interacting particle systems and my PhD is between these two areas. Throughout my PhD we will look into non-linear Stochastic Partial Differential Equations and related interacting particle systems and we will see how these two disciplines come together to describe the long-time behavior of the solution.