Emanuel Milman
Email:

emanuel.milman 'at' gmail.com or
emilman
'at' tx.technion.ac.il

Phone:
Fax:

+97248294196
+97248293388

Postal
Address:

Department
of Mathematics
Technion  Israel Institute of Technology
Haifa 32000
Israel

Office:

Amado 630

I am an Associate Professor at the Technion's Mathematics Department.
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 R^{n},
Banach spaces (possibly infinite dimensional), Riemannian manifolds
with nonnegative (Ricci)
curvature, 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, 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, geometry of isoperimetric
minimizing
surfaces,
Geometric Measure Theory, diffusion semigroup and heatkernel
estimates in
convex manifolds, optimal transport, distribution of volume in convex
bodies, classical Convex Geometry, “local
theory” of Banach
Spaces, convexity
in graphs, metric entropy and
covering numbers, empirical processes, general phenomena in high
dimensions, Integral Geometry.
Teaching Winter 2016:
Real Analysis 104165
Previous Advanced Courses Given:
HighDimensional Convex Geometric Analysis 
List of Exercises.
Isoperimetry, Sobolev and Concentration inequalities through the lens of Convexity 
List of Exercises.
Convex Bodies in High Dimension 
List of Exercises.
Isoperimetric Inequalities and Applications 
List of Exercises.
Preprints and
Manuscripts:
 with Alexander Kolesnikov, The KLS isoperimetric conjecture for generalized Orlicz balls, manuscript. [arXiv link]
 with Shahar Mendelson and Grigoris Paouris, Generalized Sudakov via Dimension Reduction  A Program, submitted. [arXiv link]
 with Alexander Kolesnikov, Riemannian metrics on convex sets with applications to Poincaré and logSobolev inequalities, to appear in Calc. Var. & PDE. [arXiv link]
 Spectral Estimates, Contractions and Hypercontractivity, to appear in J. Spectr. Theory. [arXiv link]
 Harmonic Measures on the Sphere via CurvatureDimension, to appear in Annales de la Faculté des Sciences de Toulouse. [arXiv link]
 with Alexander Kolesnikov, Sharp Poincaretype inequality for the Gaussian measure on the boundary of convex sets, to appear in GAFA Seminar Notes. [arXiv link]
 Beyond
traditional CurvatureDimension I: new model spaces for isoperimetric
and concentration inequalities in negative dimension, to appear in Trans. Amer. Math. Soc. [arXiv link]
 with Alexander Kolesnikov, Brascamp–Lieb type inequalities on weighted Riemannian manifolds with boundary, to appear in J. Geom. Anal. [arXiv link]
 with Alexander Kolesnikov, Poincare and Brunn–Minkowski inequalities on the boundary of weighted Riemannian manifolds, submitted. [arXiv link]
Publications (according to topic):
Isoperimetric
And Functional Inequalities
 Sharp
Isoperimetric Inequalities and Model Spaces for
CurvatureDimensionDiameter Condition, J. Eur. Math. Soc. 17 (5), 1041–1078, 2015. [arXiv link]
 with Alexander Kolesnikov, Isoperimetric Inequalities on Weighted Manifolds with Boundary, Doklady Akademii Nauk 464 (2), 136–140, 2015 (in Russian).
 with Alexander Kolesnikov, Remarks on KLS conjecture and Hardytype inequalities, Lecture Notes in Math. 2116, GAFA Seminar Notes 2011–2013, 273292, 2014. [arXiv link]
 with Liran Rotem, Complemented BrunnMinkowski Inequalities and Isoperimetry for Homogeneous and NonHomogeneous Measures, Adv. Math. 262, 867908, 2014. [arXiv link]
 with Franck Barthe, Transference Principles for LogSobolev and SpectralGap with Applications to Conservative Spin Systems, Comm. Math. Physics 323, 575–625, 2013. [arXiv link]
 Model Spaces for Sharp Isoperimetric Inequalities, C. R. Math. Acad. Sci. Paris 350, 897902, 2012. [pdf]
 A Proof of Bobkov's Spectral Bound For Convex Domains via Gaussian Fitting and Free Energy Estimation, Centre de Recherches Mathématiques, CRM Proceedings and Lecture Notes, Vol. 56, 181196, 2013. [arXiv link]
 Isoperimetric Bounds on
Convex Manifolds, "Concentration, Functional Inequalities and
Isoperimetry", Contemporary Mathematics 545, Amer. Math. Soc.,
195208, 2011. [arXiv
link]
 Properties
of Isoperimetric, Functional and TransportEntropy Inequalities Via
Concentration, Probab. Theory Relat. Fields 152, 475–507, 2012. [arXiv
link]
 A
converse to the Maz'ya inequality for capacities under curvature lower
bound, Springer's International Mathematical Series
Vol. 11, Around
the Research of
Vladimir Maz'ya I. Function Spaces, 321348. [arXiv
link]
 Isoperimetric
and
Concentration Inequalities  Equivalence under Curvature Lower
Bound, Duke Math. J. 154 (2), 207239, 2010. [arXiv
link]
 Concentration
and isoperimetry are equivalent assuming curvature lower bound,
C. R. Math. Acad. Sci. Paris. 347, 7376, 2009. [pdf]
 On
the role of convexity in functional and isoperimetric inequalities,
Proc. London Math. Soc. 99 (3), 3266, 2009. [arXiv
link]
 On
the role of convexity in isoperimetry, spectral gap and concentration,
Invent. Math. 177 (1), 143, 2009. [arXiv link]
 Uniform
taildecay of Lipschitz functions implies Cheeger’s
isoperimetric inequality under
convexity assumptions,
C. R. Math. Acad. Sci. Paris 346,
989994, 2008. [pdf]
 with
Sasha Sodin, An
isoperimetric inequality for uniformly logconcave
measures and uniformly convex bodies,
J. Func. Anal. 254 (5), 12351268, 2008. [arXiv
link]
Distribution of Volume in Convex Bodies
 On the meanwidth of isotropic convex bodies and their associated Lpcentroid bodies, Int. Math. Res. Not. 11, 3408–3423, 2015. [arXiv link]
 with Apostolos Giannopoulos, Mestimates for isotropic convex bodies and their Lqcentroid bodies, , Lecture Notes in Math. 2116, GAFA Seminar Notes 2011–2013, 159182, 2014. [arXiv link]
 with Bo'az
Klartag, Inner
Regularization of LogConcave Measures and SmallBall Estimates, Lecture Notes in Math. 2050, GAFA Seminar Notes 2006–2010,
267278,
2012. [arXiv link]
 with Bo'az
Klartag, Centroid
Bodies and the Logarithmic Laplace Transform  A Unified Approach, J.
Func. Anal. 262 (1), 1034, 2012. [arXiv
link]
 with Olivier Guedon, Interpolating
ThinShell and Sharp LargeDeviation Estimates For Isotropic
LogConcave Measures, Geom. Funct. Anal. 21 (5), 10431068,
2011. [arXiv
link]
 On
Gaussian marginals of uniformly convex bodies,
J. Theor. Prob. 22 (1), 256278, 2009. [arXiv
link]
 with Bo’az
Klartag, On
volume distribution in 2convex bodies,
Israel J. Math. 164, 221249, 2008. [arXiv
link]
 Dual
mixed volumes and the
Slicing Problem,
Adv. Math. 207 (2), 566598,
2006. [arXiv
link]
Contracting Maps
 with YoungHeon Kim,
A
Generalization of Caffarelli's Contraction Theorem via (reverse) Heat
Flow, Math. Annal. 354 (3), 827862, 2012. [arXiv
link]
LowDimensional
Sections of Star Bodies
 Generalized
Intersection Bodies are not equivalent,
Adv. Math. 217 (6), 28222840,
2008. [arXiv
link]
 Generalized
Intersection Bodies, J. Func. Anal. 240 (2), 530567, 2006. [arXiv
link]
 A
comment on the lowdimensional BusemannPetty problem,
Lecture Notes in Math. 1910, GAFA Seminar Notes 2004–5,
245253,
2007. [arXiv
link]
Covering
Numbers and
Metric Entropy
 A
remark on two duality relations,
Integral Equations and Operator Theory 57 (2), 217228, 2007. [arXiv
link]
Game
Theory (M.Sc. Thesis)
 Approachable
sets of vector
payoffs in stochastic games,
Games and Economic Behavior 56,
135147, 2006.
 The
semialgebraic theory of
stochastic games,
Math. Oper. Research 27,
401418, 2002.
Editorial:
Conferences Organized:
Invited Talks:
 Workshop on "Analytic Aspects of Convexity", Rome, October 2016.
 Barcelona Analysis Conference BAC16, September 2016.
 Israeli Mathematical Union annual meeting, Dead Sea, June 2016.
 Joram Memorial Seminar on “Ricci Flow and Geometrization”, Hebrew University, May 2016. [Slides]
 Workshop on "Asymptotic Geometric Analysis", Oberwolfach, February 2016.
 Colloquium at TelAviv University, Nov 2015.
 Conference on "Analytic and Probabilistic Techniques in Modern Convex Geometry", Columbia, Missouri, November 2015.
 Conference on "Convexity, Probability and Discrete Structures, a Geometric Viewpoint", ParisEst, October 2015.
 Colloquium at BenGurion University, May 2015.
 Colloquium at the Hebrew University, May 2015.
 Workshop on "Information Theory and Concentration Phenomena", IMA, Minneapolis, April 2015.
 MiniCourse, Workshop on "New developments in Optimal Transport, Geometry and Analysis", HIM, Bonn, February 2015.
 Conference in Honour of the 60th Birthday of Dominique Bakry, Toulouse. December 2014.
 Workshop on "Geometry and Probability", Kyoto, September 2014.
 Worskhop on "Isoperimetric problems between Analysis and Geometry", Pisa, June 2014.
 Asymptotic Geometric Analysis seminar, TelAviv University, May 2014.
 Workshop on "Functional Inequalities", Toulouse, April 2014.
 Asymptotic Geometric Analysis seminar, TelAviv University, January 2014.
 Israeli Mathematical Union annual meeting, Haifa University, June 2013.
 Conference on "Banach Spaces: Geometry and Analysis", Hebrew University, May 2013.
 Conference on "Complex Analysis and Dynamical Systems VI", Naharyia, May 2013.
 Workshop on "Heat Kernels, Stochastic Processes and Functional Inequalities", Oberwolfach, May 2013.
 Workshop on “Convex Geometry and its Applications", Oberwolfach, December 2012.
 Conference on “Optimal Transport and Applications", Pisa, November 2012.
 Analysis Seminar, Texas A&M, October 2012.
 Conference on “Convex Geometric Analysis”, Heraklion, September 2012.
 Conference on "Phenomena in high dimensions in
geometric analysis, random matrices, and computational geometry",
Roscoff, June 2012.
 Conference on "Interactions between Asynmptotic Geometric Analysis and Mathematical Physics", Eilat and Technion, May 2012.
 Probability Seminar, University of Geneva, April 2012.
 Plenary Talk, “Concentration inequalities and their applications”, CIRM, Luminy, January 2012.
 Plenary Talk, “Introductory workshop on quantitative geometry”, MSRI, August 2011 (cancelled).
 Geometric Analysis and Gravitation
Seminar at the MaxPlanckInstitut für Gravitationsphysik
(AlbertEinstenInsitut), Golm, July 2011.
 MiniCourse at Séminaire de
Mathématiques Supérieures on “Metric Measure
Spaces: Geometric and Analytic Aspects”, Montreal, July 2011.
 Seminar at "Discrete Analysis"
program, Cambridge, June 2011.
 Colloquium, BenGurion University, May
2011.
 Colloquium, TelAviv University, May
2011.
 Conference on "Asymptotic Geometric
Analysis and Convexity", Hagoshrim  TelAviv, April 2011.
 Short Course, Workshop on "Functional
Inequalities and Discrete Spaces", ParisEst, January 2011.
 Workshop on "Optimal Transport and
Geometric Probability", Fields Institute, November 2010.
 Workshop on "Asymptotic Geometric
Analysis", Fields Institute, September 2010.
 SAGE Workshop on "Optimal Transport
and Riemannian Geometry", University of Texas at Austin, September 2010.
 ICM Satellite Conference on
"Probability and Stochastic Processes", India, August 2010 (cancelled).
 Plenary Talk, Conference on
"Perspectives in High Dimensions", Cleveland, August 2010.
 Conference on "Asymptotic Geometric
Analysis", Euler International Mathematical Institute, St. Petersburg,
July 2010.
 Analysis Seminar, McGillConcordia,
April 2010.
 Workshop on "Volume Inequalities",
Banff, March 2010.
 Conference
on the State of
Geometry and Functional Analysis, TelAviv University, June 2009.
 Discrete
Math Seminar, Rutgers
University, April 2009.
 Colloquium,
Lehigh University, April 2009.
 Members
Seminar, Institute for
Advanced Study, February 2009.
 Functional
Analysis Seminar, Technion, January 2009.
 Colloquium,
Polytechnic Institute of
NYU, December 2008.
 Probability
Seminar, City University of New York,
October 2008.
 Geometric
Functional Analysis and
Probability Seminar, Weizmann Institute of Science, August 2008.
 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, OhioState University, May 2008.
 Differential
Geometry and Topology
Seminar, Courant Institute, April 2008.
 Conference
on Convex Geometry, University of Missouri
– Columbia, March 2008.
 PDE
Seminar, MIT,
February 2008.
 Colloquium,
Polytechnic
University,
November 2007.
 Workshop
on "Algorithmic
Convex Geometry", American Institute
of Mathematics, November 2007.
 Workshop
on
"Geometrization of Probability", Fields
Institute in Ottawa, September 2007.
 Workshop
on "Fourier
Analytic Methods in Convex Geometry", American Institute of
Mathematics, August 2007. [Slides]
 Third
annual conference
on "Phenomena in High Dimensions", Samos,
June 2007. [Slides]
 Educational
Workshop on
"Convex Geometry  Analytic aspects", Cortona,
June 2007. [Slides]
 Israel
Mathematical
Union annual meeting, BenGurion University,
May 2007.
 Geometric
and Functional
Analysis Seminar, TelAviv University,
April 2007.
 Educational
workshop on
"Convexity and Probability", Freudenstadt,
September 2006. [Slides]
 Second
annual conference
on
"Phenomena in High Dimensions", Institute Henri Poincare, Paris,
June 2006. [Slides]
 First
annual conference
on "Convex Geometry
and High Dimensional Phenomena", Vienna University of Technology, July
2005. [Slides]
 Game
Theory and Mathematical Economics
Seminar, Hebrew University,
June 2002. [Slides]
Documents:
Other Links: