Equality Cases of Geometric Inequalities (Igor Pak, UCLA)

Title: Equality Cases of Geometric Inequalities

Speaker: Igor Pak, Department of Mathematics, University of California, Los Angeles

Abstract: Geometric inequalities go back to antiquity, and so do their equality cases.  As everyone knows, the circle is the only case when the isoperimetric inequality is sharp.  But what happens to other geometric inequalities?  Apparently, as the inequalities become more general, their equality cases become more cumbersome to state and even harder to prove.  I will give a broad survey of various natural examples, with an emphasis on discrete inequalities.  I will then explain why the celebrated Alexandrov–Fenchel inequality has intractable equality cases, what does that mean, and how this can be established.  The talk is aimed at a general audience.