The study of high-dimensional convex bodies from a geometric and analytic point of view,
with an emphasis on the dependence of various parameters on the dimension stands at the …

THE ISOTROPIC POSITION AND THE REVERSE SANTALO INEQUALITY Page 1 ISRAEL
JOURNAL OF MATHEMATICS 203 (2014), 1–22 DOI: 10.1007/s11856-012-0173-2 THE …

We study some geometric properties of the $ L_q $-centroid bodies $ Z_q (\mu) $ of an
isotropic log-concave measure $\mu $ on ${\mathbb R}^ n $. For any $2\leqslant …

We propose a program for establishing a conjectural extension to the class of (origin-
symmetric) log-concave probability measures $\mu $, of the classical dual Sudakov …

We study the complexity of approximating complex zero sets of certain n-variate exponential
sums. We show that the real part, R, of such a zero set can be approximated by the (n-1)(n …

Let K be a centered convex body of volume 1 in R n. A direction θ∈ S n− 1 is called sub-
Gaussian for K with constant b> 0 if‖<⋅, θ>‖ L ψ 2 (K)⩽ b‖<⋅, θ>‖ 2. We show that if K …

We study some classical positions (minimal surface area position, minimal mean width
position, John's position, Löwner's position and the isotropic position) of a centrally …

Given any n-variate exponential sum, g, the real part of the complex zero set of g forms a sub-
analytic variety ℜ (Z (g)) generalizing the amoeba of a complex polynomial. We extend the …

Lecture notes for the introductory workshop of the program “Geometric Functional Analysis
and Applications” at the Mathematical Sciences Research Institute, Fall 2017. We present …

The workshop was dedicated to new developments in Asymptotic Geometric Analysis, the
study of high-dimensional geometric objects by analytic and probabilistic means, and its …