Elisabeth Werner

Department of Mathematics

Case Western Reserve University

Cleveland, OH 44106

Telephone: (216) 368-2901

elisabeth.werner@case.edu

I will be at ICERM, Brown University, in the Fall 2022 semester

• Curriculum Vitae
• Teaching
• Research Topics
  • Convex Geometry
  • Analysis
  • Probability
• Numberphile
• Simons Fellowship 2020-2021
• Trimester Program, Hausdorff Institut
  
  
  • The Interplay between High dimensional Geometry and Probability, Bonn, Germany, January 2021-April 2021
• Conference Organisation
  
  
  • Workshop "High Dimensional Probability", Bedlewo, Poland, June 2023.
    
    
  • Special Session "Convex geometry and PDE"
    CMS summer meeting, Memorial University, St. John's Canada June 2022.
    
    
  • Workshop "Stochastic Aspects in Convexity", University of Bochum, Germany, May 2022.
    
    
  • Calculus of Variations in Probability and Geometry, IPAM, Los Angeles, February 2022.
    
    
  • Interaction between Partial Differential Equations and Convex Geometry, BIRS Hangzhu, China, October 2021
    
    
  • Special Session: Convexity and Probability in High Dimensions,
    AMS online meeting University of Tennessee, Chattanooga October 2020.
    
    
  • 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
  
  
  • Curvature functionals on convex bodies, submitted.
    Jointly with Kateryna Tatarko.
    
    
  • Affine Surface Area, submitted.
    Jointly with Carsten Schuett.
    
    
  • Spherical convex hull of random points on a wedge,
    submitted.
    Jointly with Florian Besau, Anna Gusakova, Matthias Reitzner, Carsten Schuett, Christoph Thaele.
    
    
  • Ulam floating functions,
    submitted.
    Jointly with Chunyan Liu, Deping Ye, and Ning Zhang.
    
    
  • Geometric representation of classes of concave functions and duality
    arXiv:2112.13881, submitted.
    Jointly with G. Ivanov.
    
    
  • Best and random approximation of a convex body by a polytope
    arXiv: 2111.07306, to appear in J. of Complexity.
    Jointly with J. Prochno and C. Schuett.
    
    
  • $L_p$-Steiner quermassintegrals
    arXiv: 2110.08659, submitted.
    Jointly with Kateryna Tatarko.
    
    
  • Floating bodies and approximation of convex bodies by polytopes, Probability Surveys 19 (2022).
    
    
  • Affine invariant maps for log-concave functions
    arXiv: 2010.10889, J. Geometric Analysis 32 (2022).
    Jointly with Ben Li and C. Schuett.
    
    
  • Blaschke-Santalo inequality for many functions and geodesic barycenters of measures
    arXiv:2010.00135, Advances in Math. 396 (2022).
    Jointly with A. V. Kolesnikov.
    
    
  • Convex Floating Bodies of Equilibrium
    arXiv:2010.09006, Proceedings of the AMS 150 (2022).
    Jointly with D.I. Florentin, C. Schuett, N. Zhang.
    
    
  • Surface area deviation between smooth convex bodies and polytopes
    arXiv:1811.04656, Advances in Applied Mathematics 129 (2021).
    Jointly with J. Grote and Ch. Thaele.
    
    
  • The convex hull of random points on the boundary of a simple polytope
    arXiv: 1911.05917, to appear in J. Discrete & Computational Geometry
    Jointly with M. Reitzner and C. Schuett.
    
    
  • Pinsker inequalities and related Monge-Ampere equations for log concave functions
    arXiv:2005.07055, to appear in Indiana Univ.Math.J.
    Jointly with U. Caglar, A. V. Kolesnikov.
    
    
  • Asymptotic normality for random simplices and convex bodies in high dimensions
    arXiv: 1906.02471. Proceedings AMS 149 (2021).
    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. Journal of Geometric Analysis 31 (2021).
    Jointly with Ben Li and Carsten Schuett.
    
    
  • Constrained convex bodies with extremal affine surface areas
    arXiv: 1908.07897, Journal of Functional Analysis 279 (2020).
    Jointly with O. Giladi, H. Huang, C. Schuett
    
    
  • A Steiner formula in the $L_p$ Brunn Minkowski theory
    arXiv:1811.07225, Advances in Math. 355 (2019).
    Jointly with Kateryna Tatarko.
    
    
  • Duality of Floating and Illumination Bodies,
    arXiv:1709.02424, Indiana Univ. Math. J. 69 (2020).
    Jointly with Olaf Mordhorst.
    
    
  • Floating and Illumination Bodies for Polytopes: Duality results,
    arXiv:1709.02429, Journal of Discrete Analysis 11, (2019).
    Jointly with Olaf Mordhorst.
    
    
  • 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, Journal of London Math. Society 100 (2019).
    Jointly with Han Huang and Boaz Slomka.
    
    
  • Floating Functions,
    arXiv: 1711.11088, Israel J. Math.231 (2019).
    Jointly with Ben Li and Carsten Schuett.
    
    
  • Flag Numbers and Floating Bodies,
    arXiv:1805.11287, Advances in Math. 338 (2018).
    Jointly with Florian Besau and Carsten Schuett.
    
    
  • 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, 244--267 (2018)
    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 - 2024 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
  
  
  • current Stephanie Egler
    
    
  • 2018 - 2020 Victor Glasgo
    Thesis: "Some structural results for convex bodies:
    Gravitational Illumination bodies and stability of floating bodies"
    
    
  • 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"