Elisabeth Werner

In the Fall 2020 semester, I will be (virtually) in Berkeley at the Simons Institute

and in the Spring 2021 semester in Bonn, Germany, at the Hausdorff Institute

Curriculum Vitae
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
- Interaction between Partial Differential Equations and Convex Geometry, BIRS Hangzhu, China, October 2021
- Workshop "Stochastic Aspects in Convexity", University of Bochum, Germany, May 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
- Pinsker inequalities and related Monge-Ampere equations for log concave functions
  arXiv:2005.07055. Jointly with U. Caglar, A. V. Kolesnikov
- The convex hull of random points on the boundary of a simple polytope
  arXiv: 1911.05917. Jointly with M. Reitzner and C. 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
- Asymptotic normality for random simplices and convex bodies in high dimensions
  arXiv: 1906.02471, to appear in Proceedings AMS.
  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, Advances in Math. 355 (2019).
  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, 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.
- 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
- 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"