School of Mathematics

Institute for Advanced Study

 

 Emanuel Milman

E-mail:

emilman 'at' math.ias.edu or
emanuel.milman 'at' gmail.com

Phone:

+1-609-734-8388

Postal Address:

School of Mathematics
Institute for Advanced Study
Einstein Drive
Simonyi Hall
Princeton NJ, 08540

Office:

Simonyi 204


I am a post-doctoral member at the Institute for Advanced Study. I graduated from the Weizmann Institute of Science in July 2007, under the supervision of Prof. Gideon Schechtman.

My main research interests lie in the various aspects of Asymptotic Convex Geometric Analysis. Since its conception at the intersection of classical Convex Geometry and the "Local Theory" of Banach spaces, this field has been a source of rich and fruitful research, with connections to many other fields, such as Probability Theory, PDE, Harmonic Analysis, Differential Geometry, Mathematical Physics, Combinatorics and Graph Theory.

My PhD Thesis has its origins set in the study of several fundamental questions on the asymptotic distribution of volume inside convex bodies in n-dimensional Euclidean space, when n tends to infinity. The questions which arise in this setting are naturally related to the study of isoperimetric inequalities, metric entropy and central-limit theorems for convex domains and even Integral Geometry.

My additional research interests include Convex Geometry, the Neumann and Dirichlet Laplacians, isoperimetric minimizing surfaces, optimal transportation and the heat diffusion semi-group in convex domains, asymptotic theory of finite-dimensional normed spaces ("Local Theory"), general phenomena in high dimensions, empirical processes, Radon transforms and Harmonic Analysis on Grassmann manifolds, and their connection to Asymptotic Convex Geometric Analysis.

Publications, Preprints and Manuscripts:

  • On the role of Convexity in Isoperimetry, Spectral Gap and Concentration, 50 pages, submitted. [arXiv link]
  • On the role of Convexity in Functional and Isoperimetric Inequalities, 42 pages, submitted. [arXiv link]

Ph.D. :

  • with Sasha Sodin, Uniformly log-concave functions and isoperimetry, Journal of Functional Analysis 254 (5), 1235-1268, 2008. [arXiv link]
  • Generalized Intersection Bodies are not equivalent, Advances in Mathematics 217 (6), 2822-2840, 2008. [arXiv link]
  • A remark on two duality relations, Integral Equations and Operator Theory 57 (2), 217-228, 2007. [arXiv link]
  • On Gaussian marginals of uniformly convex bodies, Journal of Theoretical Probability, 25 pages, to appear. [arXiv link]
  • with Boaz Klartag, On volume distribution in 2-convex bodies, Israel Journal of Mathematics, 27 pages, to appear. [arXiv link]
  • A comment on the low-dimensional Busemann-Petty problem, Lecture Notes in Math. 1910, GAFA Seminar Notes 2004–5,
    245-253. [arXiv link]
  • Generalized intersection bodies, Journal of Functional Analysis 240 (2), 530-567, 2006. [arXiv link]
  • Dual mixed volumes and the Slicing Problem, Advances in Mathematics 207 (2), 566-598, 2006. [arXiv link]

M.Sc. :

  • Approachable sets of vector payoffs in stochastic games, Games and Economic Behavior 56, 135-147, 2006.
  • The semi-algebraic theory of stochastic games, Mathematics of Operations Research 27, 401-418, 2002. 

Invited Talks:

  • Fourth annual conference on "Phenomena in High Dimensions", Sevilla, June 2008.
  • Colloquium, Technion, Haifa, June 2008.
  • Fifth annual conference on “Probability in High Dimensions”, CIRM at Luminy, May 2008.
  • Colloquium, Case Western University, May 2008.
  • PDE Seminar, Ohio-State University, May 2008.
  • Differential Geometry and Topology Seminar, Courant Institute, April 2008.
  • Conference on Convex Geometry, University of Missouri – Columbia, March 2008.
  • Quantitative stability of spectral-gap and isoperimetry under perturbations of convex domains, PDE Seminar, MIT, February 2008.
  • The role of convexity in isoperimetry, spectral-gap and concentration, Colloquium, Polytechnic University, November 2007.
  • The role of convexity in isoperimetry, spectral-gap and concentration, Workshop on "Algorithmic Convex Geometry", American Institute of Mathematics, November 2007.
  • Weak Poincare inequalities and Isoperimetry in Convex Domains, Workshop on "Geometrization of Probability", Fields Institute in Ottawa, September 2007.
  • Generalized Intersection Bodies, the Low-Dimensional Busemann-Petty Problem, and what's in between, Workshop on "Fourier Analytic Methods in Convex Geometry", American Institute of Mathematics, August 2007. [Slides]
  • Isoperimetric Inequalities for Uniformly Log-Concave Measures and Uniformly Convex Bodies, Third annual conference on "Phenomena in High Dimensions", Samos, June 2007. [Slides]
  • Generalized Intersection Bodies Are Not Equivalent, Educational Workshop on "Convex Geometry - Analytic aspects", Cortona, June 2007. [Slides]
  • Isoperimetric Inequalities for Uniformly Log-Concave Measures and Uniformly Convex Bodies, Israel Mathematical Union annual meeting, Ben-Gurion Universiy, May 2007.
  • Isoperimetric Inequalities for Uniformly Log-Concave Measures and Uniformly Convex Bodies, Geometric and Functional Analysis Seminar, Tel-Aviv University, April 2007.  
  • Generalized Intersection Bodies and the low dimensional Busemann-Petty Problem, educational workshop on "Convexity and Probability", Freudenstadt, September 2006. [Slides]
  • Gaussian Marginals of Uniformly Convex Bodies, Second annual conference on "Phenomena in High Dimensions", Institute Henri Poincare, Paris, June 2006. [Slides]
  • Covering Numbers and the Duality of Entropy, Geometric Functional Analysis and Probability Seminar, Weizmann Institute of Science, April 2006.
  • Dual Mixed Volumes and the Slicing Problem, First annual conference on "Convex Geometry and High Dimensional Phenomena", Vienna University of Technology, July 2005. [Slides]
  • The Semi-Algebraic Theory of Stochastic Games, Game Theory and Mathematical Economics Seminar, Hebrew University, June 2002. [Slides]

CV: 

          [Click Here]

Links: