
Curriculum Vitae
 Teaching
 Research Topics
 Convex Geometry
 Analysis
 Probability

Applications of the above to Approximation Theory, Mathematical Physics, and Quantum
Information Theory
 Conference Organisation
 MiniWorkshop ``Perspectives in Highdimensional Probability and Convexity", Oberwolfach, Germany, February 2017.
 Special Session on "Discrete Structures: Analysis and Applications", Minneapolis/St. Paul, October, 2016.
 Special Session on "Probabilistic and Analytic tools in Convexity", Athens, Georgia, March 2016.
 Affine Geometric Analysis, BIRS Oaxaca, September 2015.
 Asymptotic Geometric Analysis, Case Western Reserve University, August 2015.
 Special Session on "High dimensional convexity and applications", San Francisco, October 2526, 2014.
 Interplay of convex geometry and Banach space theory, Banff, Canada, March 2013.
 Invariants in convex geometry and Banach space theory, AIM, Palo Alto, August 2012.
 Geometry of Quantum Entanglement, CIRM, Marseille, January 2012.
 Perspectives in High Dimensions, Cleveland, Ohio, August 2010.
 Geometry of Quantum Entanglement, Oberwolfach, Germany, December 2009.
 Affine Convex Geometric Analysis, Banff, Canada, January 2009.
 Fourier Analytic and Probabilistic Methods in Functional Analysis and Convexity, Kent, Ohio, August 2008.
 Special Session on Convex Geometry, Hoboken, New Jersey, April 2007.
 Asymptotic Analysis and Applications, Paris, France, August, 2006.
 Convex Geometric Analysis, Banff, Canada, July 2004.
 Special Session "Analytic Convex Geometry", Lawrenceville, New Jersey, April 2004.
 Special Session in "Convex Geometry", Boston, Massachusetts, October 2002.
 Special Session on "Invariance Convex Geometry", Lowell, Massachusetts, April 2000.
 Special Session on "Harmonic Analysis and Convexity", Memphis, Tennessee, March 1997.
 Publications

The Spherical Convex Floating Body
Advances in Mathematics 301, 867901 (2016)
Jointly with Florian Besau.

The Surface Area Deviation of the Euclidean Ball and a Polytope
Journal of Theoretical Probability DOI 10.1007/s1095901607019, 124 (2016)
Jointly with Steven Hoehner and C.Schuett.

Mixed fdivergence for multiple pairs of measures
Canadian Mathematical Bulletin DOI 10.4153/CMB20160503 (2016)
Jointly with Deping Ye.

Affine invariant points
Israel J. Math. 208, 163192 (2015)
Jointly with M. Meyer and C. Schuett.

Dual affine invariant points
Indiana J. Math. 64, 735768 (2015)
Jointly with M. Meyer and C. Schuett.

Functional versions of L_paffine surface area and entropy inequalities
IMRN, doi:10.1093/imrn/rnv151 (2015)
Jointly with U.Caglar, M.Fradelizi, O.Guedon, J.Lehec and C.Schuett.

Mixed fdivergence and inequalities for log concave functions
Proc. London Math. Soc. doi: 10.1112/plms/pdu055, (2014)
Jointly with Umut Caglar.

Divergence for sconcave and log concave functions
Advances in Mathematics 257, 219247 (2014)
Jointly with Umut Caglar.

fDivergence for convex bodies
Proceedings of the "Asymptotic Geometric Analysis" workshop, Fields Institute, Toronto 2012

On the approximation of a polytope by its dual Lpcentroid bodies
Indiana Univ. Math. J. 62, 235247 (2013)
Jointly with G. Paouris.

Relative entropies for convex bodies
TRANSACTIONS OF THE AMS 366, 28892906 (2014)
Jointly with J. Jenkinson.

Renyi Divergence and Lpaffine surface area for convex bodies
Advances in Mathematics 230, 10401059 (2012)

Functional affineisoperimetry and an inverse logarithmic Sobolev inequality
Journal of Functional Analysis 262, 41814204 (2012)
Jointly with S. ArtsteinAvidan, B. Klartag and C. Schuett

Relative entropy of cone measures and Lp centroid bodies
PROCEEDINGS LONDON MATH. SOC. 104 (2012), no. 2, 253–286.
Jointly with G. Paouris.

A note on Mahler's conjecture
INTERNATIONAL MATH. RESEARCH NOTICES, (2012), no. 1, 1–16.
Jointly with S. Reisner and C. Schuett.

Uniform estimates for order statistics and Orlicz functions
POSITIVITY, 16 (2012), no. 1, 1–28.
Jointly with Y. Gordon, A. Litvak and C. Schuett.

On the Homothety Conjecture
Indiana Univ. Math. J. 60 No. 1, 1–20, (2011)
Jointly with Deping Ye.

New affine measures of symmetry for convex bodies
ADVANCES IN MATHEMATICS 228, 2920–2942 (2011)
Jointly with M. Meyer and C. Schuett.

How often is a random quantum state kentangled
J. PHYSICS A: MATH. THEOR. 44 (2011)
Jointly with S. Szarek and K. Zyczkowski.

Hastings' additivity counterexample via Dvoretzky's theorem
COMMUNICATIONS IN MATHEMATICAL PHYSICS 305 (2011)
Jointly with G. Aubrun and S. Szarek.

Nonadditivity of Renyi entropy and Dvoretzky's Theorem
JOURNAL OF MATHEMATICAL PHYSICS 51 (2010) 022102 and
VIRTUAL JOURNAL OF QUANTUM INFORMATION 10 (2010)
Jointly with G. Aubrun and S. Szarek.

Inequalities for mixed paffine surface area
MATHEMATISCHE ANNALEN 347, 703737 (2010)
Jointly with Deping Ye.

New Higher Order Equiaffine Invariants
ISRAEL JOURNAL OF MATHEMATICS 171, 221235 (2009)
Jointly with A. Stancu.

Bipartite states of low rank are almost surely entangled
J. PHYS. A: MATH. THEOR. 42 (2009) 095303
Jointly with M. B. Ruskai

New Lp affine isoperimetric inequalities
ADVANCES IN MATHEMATICS 218, 762780 (2008)
Jointly with Deping Ye

Geometry of sets of quantum maps: a generic positive map acting on a highdimensional system is not completely positive
J. MATH. PHYS. 49, no. 3, 032113 (2008)
Jointly with S. Szarek and K. Zyczkowski

On Lp affine surface areas
INDIANA UNIVERSITY MATH. J. 56, 23052324 (2007)

On the minimum of several random variables
PROCEEDINGS AMERICAN MATHEMATICAL SOCIETY 134, 36653675 (2006)
Jointly with Y. Gordon, A. Litvak and C. Schuett

Floating bodies and Illumination bodies
PROCEEDINGS OF THE CONFERENCE "INTEGRAL GEOMETRY AND CONVEXITY"
Wuhan 2004, World Scientific, Singapore (2006)

Approximation of the Euclidean ball by a polytope
STUDIA MATHEMATICA 173, 118 (2006)
Jointly with M. Ludwig and C. Schuett

Minima of sequences of Gaussian random variables
COMPTES RENDUS DE L'ACADEMIE DES SCIENCES PARIS, Ser.I 340, 445448 (2005)
Jointly with Y. Gordon, A. Litvak and C. Schuett

Surface bodies and p  affine surface area
ADVANCES IN MATHEMATICS 187, 98145 (2004)
Jointly with C. Schuett.

Geometry of spaces between polytopes and related zonotops
BULLETIN DES SCIENCES MATHEMATIQUES 126, 733762 (2002)
Jointly with Y. Gordon, A. Litvak and C. Schuett

Orlicz norms of sums of random variables
ANNALS OF PROBABILITY 30 , 18331853 (2002)
Jointly with Y. Gordon, A. Litvak and C. Schuett

The p  affine surface area and geometric interpretations
RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO (2) Suppl. 70, part II, 367382 (2002)

Random polytopes of points chosen from the boundary of a convex body
GAFA SEMINAR NOTES, LECTURE NOTES IN MATHEMATICS 1807, Springer, 241422 (2002)
Jointly with C. Schuett

An Analysis of Completely positive Trace preserving maps on M2
LINEAR ALGEBRA AND ITS APPLICATIONS 347, 159187 (2002)
Jointly with M. B. Ruskai and S. Szarek

Dropping a vertex or a facet from a convex polytope
FORUM MATHEMATICUM 13, 359378 (2001)
Jointly with S. Reisner and C. Schuett

Random polytopes with vertices on the boundary of a convex body
COMPTES RENDUS DE L'ACADEMIE DES SCIENCES PARIS 331, 697201 (2000)
Jointly with C. Schuett

Study of a class of regularizations of 1/x using Gaussian integrals
SIAM J.OURNAL OF MATHEMATICAL ANALYSIS vol.32, no. 2, 435463 (2000)
Jointly with M. B. Ruskai

One Dimensional Regularizations of the Coulomb Potential with Application to Atoms in Strong Magnetic Fields
DIFFERENTIAL EQUATIONS AND MATHEMATICAL PhYSICS, 4351 International Press, (2000)
Jointly with M. B. Ruskai and R. Brummelhuis

On the paffine surface area
ADVANCES IN MATHEMATICS 152, 288313 (2000)
Jointly with M. Meyer

A general geometric construction of affine surface area
STUDIA MATHEMATICA 132, 227238 (1999)

Confidence Regions for Means of Multivariate Normal Distributions and a nonsymmetric Correlation Inequality for Gaussian measure
JOURNAL OF MULTIVARIATE ANALYSIS 68, 193211 (1999)
Jointly with S. Szarek

The Santaloregions of a convex body
TRANSACTIONS OT THE AMS 350, 45694591 (1998)
Jointly with M. Meyer

The illumination body of almost polygonal bodies
GEOMETRIAE DEDICATA 64, 343354 (1997)

The convex floating body
MATH. SCAND. 66 275290 (1990)
Jointly with C. Schuett
 Projects
 2000  2018 NSF: Convexity and Applications
 2007  2011 BSF: Applications of the methods of Asymptotic Geometric Analysis to Symplectic Geometry, Functional Inequalities and Metric Entropy
 2007  2012 FRG Collaborative Research Grant: Fourier Analytic and Probabilistic Methods in Geometric Functional Analysis and Convexity
 1994  1997 NSF: Convexity and Applications
 1989  1993 NSF: Banach Spaces and Convexity
 Ph.D Students

Since 2014
Ben Li

2014  2016 Steven Hoehner,
Thesis: "The surface area deviation of the Euclidean ball and a polytope"

2011  2014 Umut Caglar
Thesis: "Divergence and Entropy inequalities for log concave functions"

2009  2013 Justin Jenkinson
Thesis: "Convex Geometric Connections to Information Theory"

2006  2009 Deping Ye
Thesis: "Topics in Convex Geometry and Phenomena in High Dimension"

2001  2003 Mark Meckes
Thesis: "Random Phenomena in Finite Dimensional Normed Spaces"