Elisabeth Werner

A picture of Professor Werner.

Photo by MFO

Department of Mathematics

Case Western Reserve University

Cleveland, OH 44106

Telephone: (216) 368-2901

elisabeth.werner@case.edu

 
  • Curriculum Vitae
  • Teaching
  • Research Topics
    • Convex Geometry
    • Analysis
    • Probability
    • Applications of the above to Approximation Theory, Mathematical Physics, and Quantum Information Theory
  • Conference Organisation
    • 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, Tennissee, March 1997.
  • Publications
    • On the mixed $f$-divergence for multiple pairs of measures
      Jointly with Deping Ye.
    • Affine invariant points
      Jointly with M. Meyer and C. Schuett.
    • f-Divergence for convex bodies
      Proceedings of the ``Asymptotic Geometric Analysis" workshop, Fields Institute, Toronto 2012
    • On the approximation of a polytope by its dual Lp-centroid bodies
      to appear in Indiana Univ. Math. J. Jointly with G. Paouris.
    • Relative entropies for convex bodies
      to appear in TRANSACTIONS OF THE AMS
      Jointly with J. Jenkinson.
    • Renyi Divergence and Lp-affine surface area for convex bodies
      Advances in Mathematics 230, 1040--1059 (2012)
    • Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality
      Journal of Functional Analysis 262, 4181-4204 (2012)
      Jointly with S. Artstein-Avidan, 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 k-entangled
      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.
    • Non-additivity 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 p-affine surface area
      MATHEMATISCHE ANNALEN 347, 703-737 (2010)
      Jointly with Deping Ye.
    • New Higher Order Equiaffine Invariants
      ISRAEL JOURNAL OF MATHEMATICS 171, 221-235 (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, 762-780 (2008)
      Jointly with Deping Ye
    • Geometry of sets of quantum maps: a generic positive map acting on a high-dimensional 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, 2305-2324 (2007)
    • On the minimum of several random variables
      PROCEEDINGS AMERICAN MATHEMATICAL SOCIETY 134, 3665-3675 (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, 1-18 (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, 445-448 (2005)
      Jointly with Y. Gordon, A. Litvak and C. Schuett
    • Surface bodies and p - affine surface area
      ADVANCES IN MATHEMATICS 187, 98-145 (2004)
      Jointly with C. Schuett.
    • Geometry of spaces between polytopes and related zonotops
      BULLETIN DES SCIENCES MATHEMATIQUES 126, 733-762 (2002)
      Jointly with Y. Gordon, A. Litvak and C. Schuett
    • Orlicz norms of sums of random variables
      ANNALS OF PROBABILITY 30 , 1833-1853 (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, 367-382 (2002)
    • Random polytopes of points chosen from the boundary of a convex body
      GAFA SEMINAR NOTES, LECTURE NOTES IN MATHEMATICS 1807, Springer, 241-422 (2002)
      Jointly with C. Schuett
    • An Analysis of Completely positive Trace preserving maps on M2
      LINEAR ALGEBRA AND ITS APPLICATIONS 347, 159-187 (2002)
      Jointly with M. B. Ruskai and S. Szarek
    • Dropping a vertex or a facet from a convex polytope
      FORUM MATHEMATICUM 13, 359-378 (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, 697-201 (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, 435-463 (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, 43-51 International Press, (2000)
      Jointly with M. B. Ruskai and R. Brummelhuis
    • On the p-affine surface area
      ADVANCES IN MATHEMATICS 152, 288-313 (2000)
      Jointly with M. Meyer
    • A general geometric construction of affine surface area
      STUDIA MATHEMATICA 132, 227-238 (1999)
    • Confidence Regions for Means of Multivariate Normal Distributions and a non-symmetric Correlation Inequality for Gaussian measure
      JOURNAL OF MULTIVARIATE ANALYSIS 68, 193-211 (1999)
      Jointly with S. Szarek
    • The Santalo-regions of a convex body
      TRANSACTIONS OT THE AMS 350, 4569-4591 (1998)
      Jointly with M. Meyer
    • The illumination body of almost polygonal bodies
      GEOMETRIAE DEDICATA 64, 343-354 (1997)
  • Projects
    • 2000 - 2015 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 2011 Umut Caglar
    • 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"