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Thursday, September 18, 2014

**Abstract:** In the theory of representations of Galois groups, a central object of study is Mazur's universal deformation space. It is an object that parametrizes Galois representations in a continuous way. There are many unknown questions and conjectures about this space. For example: What is its dimension? Can we describe the smooth points? Is the subset constructed via modular forms a dense subspace? In this talk we will give an overview of the theory of deformations of Galois representations, and discuss some progress on the above questions.