Elisabeth Werner

A picture of Professor Werner.

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
    • Numberphile https://youtu.be/c4pgWd8V8HU
  • Conference Organisation
    • New Perspectives and Computational Challenges in High Dimensions, Oberwolfach, Germany February 2020.
    • Symmetry and Convexity in geometric inequalities, AIM, San Jose, May 2019.
    • Special Session: Convex Geometry and Functional Inequalities , University of Delaware, September 2018
    • Convex Geometry and Geometric Functional Analysis, TSIMF, Sanya, China, May 2018
    • Emerging Trends in Geometric Functional Analysis, Banff, Canada, March 2018
    • Special Session on "Probability in Convexity and Convexity in Probability", OSU, Columbus, OH March 2018
    • Connections for Women: geometry and probability in high dimensions , MSRI, Berkeley, California, August 2017
    • "Perspectives in High-dimensional 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 25-26, 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 convex hull of random points on the boundary of a simple polytope
      arXiv: 1911.05917 Jointly with M. Reitzner and C. Sch\"utt
    • Constrained convex bodies with extremal affine surface areas
      arXiv: 1908.07897 Jointly with O. Giladi, H. Huang, C. Sch\"utt
    • Asymptotic normality for random simplices and convex bodies in high dimensions
      arXiv: 1906.02471
      Jointly with D.Alonso-Gutierrez, F.Besau, J.Grote, Z.Kabluchko, M.Reitzner, C.Thaele, B.Vritsiou.
    • The Loewner function of a log-concave function
      arXiv: 1904.01211, to appear in Journal of Geometric Analysis
      Jointly with Ben Li and Carsten Schuett.
    • A Steiner formula in the $L_p$ Brunn Minkowski theory
      arXiv:1811.07225
      Jointly with Kateryna Tatarko.
    • Surface area deviation between smooth convex bodies and polytopes
      arXiv:1811.04656
      Jointly with Julian Grote and Christoph Thaele.
    • Data depth and floating body,
      arXiv:1809.10925, Statistics Surveys 13 (2019), 52-118
      Jointly with Stanislav Nagy and Carsten Schuett.
    • Ulam Floating bodies,
      arXiv:1803.08224, to appear in Journal of London Math. Society
      Jointly with Han Huang and Boaz Slomka.
    • Floating Functions,
      arXiv: 1711.11088, to appear in Israel J. Math.
      Jointly with Ben Li and Carsten Schuett.
    • Duality of Floating and Illumination Bodies for Polytopes,
      arXiv:1709.02429, to appear in Journal of Discrete Analysis
      Jointly with Olaf Mordhorst.
    • Flag Numbers and Floating Bodies,
      arXiv:1805.11287, Advances in Math. 338 (2018)
      Jointly with Florian Besau and Carsten Schuett.
    • Duality of Floating and Illumination Bodies,
      arXiv:1709.02424, to appear in Indiana J. Math.
      Jointly with Olaf Mordhorst.
    • Approximation of smooth convex bodies by random polytopes,
      Electronic Journal of Probability 23, (2018)
      Jointly with Julian Grote.
    • The Floating Body in Real Space Forms,
      Journal Diff. Geometry, Vol. 110, No. 2 (2018), 187-220.
      Jointly with Florian Besau.
    • Weighted floating bodies and polytopal approximation,
      TAMS 370, (2018), 7129--7148
      Jointly with F. Besau and M. Ludwig.
    • On the geometry of projective tensor products,
      Journal of Functional Analysis 273, (2017), 471--495
      Jointly with O. Giladi, J. Prochno, C. Schuett and N. Tomczak-Jaegermann.
    • Stability results for some geometric inequalities and their functional versions,
      The IMA Volumes in Mathematics and its Applications 161: Convexity and Concentration, Springer (2017)
      Jointly with Umut Caglar.
    • The Spherical Convex Floating Body
      Advances in Mathematics 301, 867-901 (2016)
      Jointly with Florian Besau.
    • The Surface Area Deviation of the Euclidean Ball and a Polytope
      Journal of Theoretical Probability 31, (2018), 244--267 (2018)
      DOI 10.1007/s10959-016-0701-9, 1--24 (2016)
      {\bf 31}, (2018), 244--267 Jointly with Steven Hoehner and C.Schuett.
    • Mixed f-divergence for multiple pairs of measures
      Canadian Mathematical Bulletin DOI 10.4153/CMB-2016-050-3 (2016)
      Jointly with Deping Ye.
    • Affine invariant points
      Israel J. Math. 208, 163-192 (2015)
      Jointly with M. Meyer and C. Schuett.
    • Dual affine invariant points
      Indiana J. Math. 64, 735-768 (2015)
      Jointly with M. Meyer and C. Schuett.
    • Functional versions of L_p-affine 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 f-divergence and inequalities for log concave functions
      Proc. London Math. Soc. doi: 10.1112/plms/pdu055, (2014)
      Jointly with Umut Caglar.
    • Divergence for s-concave and log concave functions
      Advances in Mathematics 257, 219-247 (2014)
      Jointly with Umut Caglar.
    • 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
      Indiana Univ. Math. J. 62, 235-247 (2013)
      Jointly with G. Paouris.
    • Relative entropies for convex bodies
      TRANSACTIONS OF THE AMS 366, 2889--2906 (2014)
      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)
    • The convex floating body
      MATH. SCAND. 66 275-290 (1990) Jointly with C. Schuett
  • Projects
    • 2000 - 2021 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 2018 Victor Glasgo
    • 2014 - 2018 Ben Li
      Thesis: "Convex analysis and its application to quantum information theory"
    • 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"