Skip to main content
Skip to main menu


Geometry Seminar: Galyna Livshitz, Georgia Tech

Date and time:
Room 304 Boyd Graduate Studies Bldg.


Speaker: Galyna Livshitz, Georgia Tech

Title: On the role of symmetry in isoperimetric-type inequalities

Abstract: In the recent y ears, a number of conjectures has appeared, concerning the improvement of the inequalities of Brunn-Minkowski type under the additional assumptions of symmetry; this includes the B-conjecture, the Gardner-Zvavitch conjecture of 2008, the Log-Brunn-Minkowski conjecture of 2012, and some variants. The conjecture of Gardner and Zvavitch, also known as dimensional Brunn-Minkowski conjecture, states that even log-concave measures in Rn are in fact 1 - concave with respect to the addition of symmetric convex n sets. In this talk we shall prove that the standard Gaussian measure enjoys 1 concavity with respect to 2n centered convex sets. The improvements to the case of general log-concave measures shall be discussed as well: under certain compactness assumption, we show that any symmetric log-concave measure is indeed better-than-log-concave with respect to the addition of symmetric convex sets. This is a joint work with A. Kolesnikov.

Support us

We appreciate your financial support. Your gift is important to us and helps support critical opportunities for students and faculty alike, including lectures, travel support, and any number of educational events that augment the classroom experience. Click here to learn more about giving.

Every dollar given has a direct impact upon our students and faculty.