Elisabeth Werner Department of Mathematics Case Western Reserve University Cleveland,OH 44106 Tel: 216 368 2901 elisabeth.werner@case.edu

• convex geometry
• analysis
• probability
• applications of the above to approximation theory, mathematical physics, quantum information theory

Conference Organisation

• 12/2009 Geometry of Quantum Entanglement in Oberwolfach
  
• 01/2009 Affine Convex Geometric Analysis in Banff
  
• 08/2008 Fourier analytic and probabilistic methods in functional analysis and convexity in Kent, OH
  
• 04/2007 Special Session on Convex Geometry in Hoboken, NJ
  
• 08/2006 Asymptotic Analysis and Applications in Paris
  
• 07/2004 Convex Geometric Analysis in Banff
  
• 04/2004 Special Session "Analytic Convex Geometry" in Lawrenceville, NJ
  
• 10/2002 Special Session in "Convex Geometry" in Boston
  
• 04/2000 Special Session on "Invariance in Convex Geometry" in Lowell, Ma
  
• 03/1997 Special Session on "Harmonic Analysis and Convexity" in Memphis
  

Selected Talks

• Convex bodies: Best and Random approximation
  Invited address at the AMS Sectional Meeting, Stevens College, Hoboken, 2007
  

Projects

• 2000 - 2012 NSF Convexity and Applications
• 2007 - 2011 BSF Applications of the methods of Asymptotic Geometric Analysis to
  Symplectic Geometry, Functional Inequalities and Metric Entropy
• 2007 - 2010 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

PhD Students

• 2001 - 2003 Mark Meckes
  Thesis "Random Phenomena in Finite Dimensional Normed Spaces"
• 2006 - 2009 Deping Ye
  Thesis "Topics in Convex Geometry and Phenomena in High Dimension"
• Since 2009 Justin Jenkinson
  

Publications

• Non-additivity of Renyi entropy and Dvoretzky's Theorem
  arXiv:0910.1189
  Jointly with Guillaume Aubrun and Stanislaw Szarek.
• Relative entropy of cone measures and $L_p$ centroid bodies
  arXiv:0909.4361
  Jointly with Grigoris Paouris.
• Inequalities for mixed p-affine surface area
  arXiv:0812.4550v1.
  Jointly with Deping Ye.
• Uniform estimates for order statistics and Orlicz functions
  arXiv:0809.2989v1.
  Jointly with Y. Gordon, A. Litvak and C. Schuett.
• 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 (with C. Sch\"{u}tt),
  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 ${\mathcal M}_2$
  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 {G}aussian 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).