emanuel.milman ‘at’ gmail.com or
emilman ‘at’ tx.technion.ac.il
- Phone: +972-4-8294196
- Fax: +972-4-8293388
- Postal Address:
Department of Mathematics
Technion – I.I.T.
- Office: Amado 630
My main research interests lie in the various aspects of Asymptotic Convex Geometric Analysis. This is the study of geometric structures satisfying appropriate convexity conditions from a geometric and analytic point of view, with an emphasis on the asymptotic dependence (or independence) of various parameters on the underlying dimension. Examples of such structures include bounded convex domains in Euclidean space Rn, Banach spaces (possibly infinite dimensional), Riemannian manifolds with non-negative (Ricci) curvature, metric-measure spaces satisfying a Curvature-Dimension condition, and other generalizations.
Since its conception at the intersection of classical Convex Geometry and the local theory of Banach spaces, the field of Asymptotic Convex Geometric Analysis has been evolving constantly, and has uncovered connections to many other fields, such as Probability Theory, PDE, Riemannian Geometry, Optimal-Transport, Harmonic Analysis, Mathematical Physics, Combinatorics, Graph Theory and Learning Theory.
Some of my related research interests include isoperimetric, functional and concentration inequalities, the interplay between geometry and spectral properties of Riemannian manifolds, diffusion semi-group and heat-kernel estimates in convex manifolds, Optimal-Transport, distribution of volume in convex bodies, classical and modern Convex Geometry, “local theory” of Banach Spaces, convexity in discrete spaces and in Statistical Mechanics, metric entropy and covering numbers, empirical processes, general phenomena in high dimensions, Integral Geometry.