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, mathemtical physics, quantum information theory

Affine convex geometric analysis

Convex bodies: Best and Random approximation

Inequalities for mixed p-affine surface area (with Deping Ye), arXiv:0812.4550v1

Bipartite states of low rank are almost surely entangled (with M. B. Ruskai), arXiv:0812.0405v1

Uniform estimates for order statistics and Orlicz functions (with Y. Gordon, A. Litvak and C. Sch\"{u}tt), arXiv:0809.2989v1

New L_p affine isoperimetric inequalities (with Deping Ye), Advances in Math. 218 (2008), no. 3, 762-780

Geometry of sets of quantum maps: a generic positive map acting on a high-dimensional system is not completely positive (with S. Szarek and K. Zyczkowski), J. Math. Phys. 49 (2008), no. 3, 032113

New Higher Order Equiaffine Invariants (with A. Stancu), to appear in Israel J. Math.

On L_p affine surface areas, Indiana Univ. Math. J. 56, no.5 (2007), 2305-2324

On the minimum of several random variables (with Y. Gordon, A. Litvak and C. Sch\"{u}tt), Proc. Amer. Math. Soc. 134 (2006), no. 12, 3665-3675

Floating bodies and Illumination bodies, Integral Geometry and Convexity, Proc. Conf. Wuhan, E. Grinberg, S. Li, G. Zhang, J. Zhou editors, World Scientific Pub. (2006)

Approximation of the Euclidean ball by a polytope (with M. Ludwig, C. Sch\"{u}tt), Studia Math. 173 (2006), 1-18

Minima of sequences of Gaussian random variables (with Y. Gordon, A. Litvak and C. Sch\"{u}tt), C.R.Acad.Sci.Paris, Ser.I 340 (2005), 445-448

Surface bodies and $p$- affine surface area (with C. Sch\"{u}tt), Advances in Math. 187 (2004), 98-145

Geometry of spaces between polytopes and related zonotops (with Y. Gordon, A. Litvak and C. Sch\"{u}tt), Bulletin des sciences math\'ematiques, 126(2002), 733-762

Orlicz norms of sums of random variables (with Y. Gordon, A. Litvak and C. Sch\"{u}tt), Annals of Probability 30 (2002), 1833-1853

The $p$- affine surface area and geometric interpretations, Rendiconti Circ. Mat. Palermo Serie II, 70 (2002), 367-382

Random polytopes of points chosen from the boundary of a convex body (with C. Sch\"{u}tt), GAFA Seminar Notes (2002), Lecture Notes in Mathematics 1807, Springer-Verlag, 241-422

An Analysis of Completely positive Trace preserving maps on ${\mathcal M}_2$ (with M. B. Ruskai and S. Szarek), Linear Algebra and its Applications 347 (2002), 159-187

Dropping a vertex or a facet from a convex polytope (with S. Reisner and C. Sch\"{u}tt), Forum Math. 13 (2001), 359-378

Random polytopes with vertices on the boundary of a convex body (with C. Sch\"{u}tt), Comptes Rendus de l'Acad\'emie des Sciences Paris 331 (2000), 697-201

Study of a class of regularizations of $1/|x|$ using {G}aussian integrals, (with M. B. Ruskai), SIAM J. of Math. Analysis vol.32, no. 2 (2000), 435-463

One Dimensional Regularizations of the Coulomb Potential with Application to Atoms in Strong Magnetic Fields, (with M. B. Ruskai and R. Brummelhuis), Differential Equations and Mathematical Physics, ed. by G.Weinstein and R. Weikard, 43-51, International Press, (2000)

On the p-affine surface area (with M. Meyer), Advances in Math. 152 (2000), 288-313

A general geometric construction of affine surface area, Studia Math.132 (3) (1999), 227-238

Confidence Regions for Means of Multivariate Normal Distributions and a non-symmetric Correlation Inequality for Gaussian measure (with S. Szarek), Journal of Multivariate Analysis 68 (1999), 193-211

The Santalo-regions of a convex body (with M. Meyer), Transactions of the AMS 350, no.11 (1998), 4569-4591

The illumination body of almost polygonal bodies, Geom. Ded. 64 No. 3 (1997), 343-354