The classical Borsuk-Ulam theorem asserts that any continuous map from S^n to R^n sends at least one pair of antipodal points to the same point. In this talk, I will first recall Borsuk-Ulam theorem and its equivalent versions as well as some interesting and amusing applications. Then I shall talk about Gromov's waist inequality, which could be viewed (at least from one perspective) as a far-reaching generalization of Borsuk-Ulam theorem.  The concept of waist also appeared in other formats such as the distortion of knots. This talk is mainly based on an essay by Larry Guth and as advertised by him, the circle of ideas around waist inequality should and will be more and more fundamental and important in geometry and beyond.

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