Hypercontractive inequalities and their extensions

Hypercontractive inequalities are a class of functional inequalities that strengthen the well-known Holder inequalities. These inequalities have found many applications in functional analysis, probability theory, discrete Fourier analysis, theoretical computer science, etc., especially in dealing with extremal problems in the geometry of high-dimensional spaces. In this talk, we will introduce hypercontractive inequalities and their extensions, including the information-theoretic characterization of hypercontractive inequalities, a non-linear strengthening of hypercontractive inequalities, and the opposite version of hypercontractive inequalities, called anti-contractive inequalities.

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