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Title: Hypercontractivity for global functions

Abstract: The hypercontractivity theorem on the Boolean cube is a central tool in the analysis of Boolean functions.
     In the talk we will:
1) Explain the theorem and its main implications.
2) Show how we generalize the hypercontractivity theorem to other settings, such as the symmetric group. 
3) Describe applications of our machinery to extremal combinatorics, isoperimetric inequalities, and multiplicative combinatorics.