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The colloquium typically meets Mondays at 4:00 PM in Room 617 on the sixth floor of Wachman Hall.
The colloquium is preceded by tea starting at 3:30 in the Faculty Lounge, adjacent to Room 617. Click on title for abstract.
Kavita Ramanan, Brown University
The hyperplane conjecture in convex geometry is a statement about the volume of a convex body and that of its hyperplane sections. Taking a measure-theoretic perspective to this problem, Bourgain highlighted the importance of the notion of a $\psi_2$-convex body, which captures integrability properties of linear images of the volume measure on the body. Despite this notion being introduced more than a quarter century ago, there are not many examples of such bodies. We describe several results on the $\psi_2$ (or more generally, $\psi_\alpha$) behavior of Schatten balls and their marginals, and their relation to the hyperplane conjecture. Along the way, we also establish some properties of the Haar measure on the orthogonal group that may be of independent interest. This is joint work with Grigoris Paouris.
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