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1. Glossary
A convex body is, technically, a closed and bounded convex set with nonzero volume. convex geometry The study of convex shapes, usually in Euclidean space.
http://www.math.ucdavis.edu/glossary.html

Extractions: Index: A B C D ... Z A algebraic geometry Traditionally, the geometry of solutions in the complex numbers to polynomial equations. Modern algebraic geometry is also concerned with algebraic varieties, which are a generalization of such solution sets, as well as solutions in fields other than complex numbers, for example finite fields. algebraic topology The branch of topology concerned with homology and other algebraic models of topological spaces algebraic variety A space which is locally the solution locus to a set of polynomial equations. Algebraic varieties are for algebraic geometry topological spaces are for topology manifolds . However, algebraic varieties may also have complicated singular sets and may be parametrized with rings other than the complex numbers. (For the technical reason that the real numbers are not algebraically closed, one does not consider algebraic varieties over the real numbers in the straightforward sense.) alternating-sign matrix A matrix of 0's, 1's, and -1's such that, if the zeroes are deleted from any row or column, the remaining entries alternate in sign and begin and end with 1. almost complex manifold A manifold with the property that each tangent space has the structure of a complex vector space, but the complex structures are not necessarily compatible with true complex coordinates as they are for a complex manifold.

2. Roman Vershynin: Papers
The main result represents a new connection between the local asymptotic convex geometry (study of sections of convex bodies) and the global asymptotic convex
http://www.math.ucdavis.edu/~vershynin/papers/papers.html

Extractions: Dependencies among the coefficients in frame expansions often allow for better performance comparing to bases under random losses of coefficients. We show that for any n-dimensional frame, any source can be linearly reconstructed from only n log n randomly chosen frame coefficients, with a small error and with high probability. Thus every frame expansion withstands random losses better (for worst case sources) than the orthogonal basis expansion, for which the n log n bound is attained.

3. Conference03
It is dedicated to questions of asymptotic geometric analysis, to the interactions between finite(high-)dimensional Banach spaces and convex geometry.
http://www.math.uni-kiel.de/convex/

Extractions: Hebrew University Jerusalem The photos are now available. The conference is organized jointly by the Landau Center at the Hebrew University and the University of Kiel. It is dedicated to questions of asymptotic geometric analysis, to the interactions between finite-(high-)dimensional Banach spaces and convex geometry. The emphasis will be to compare recent results and ideas in both areas and to study the methods used, in particular those of analytic and probabilistic nature. Typical topics would include e.g. convex geometric inequalities, volume calculations, measure transportation, random constructions of convex bodies, Dvoretzky's theorem and its ramifications, symmetrizations of convex bodies, approximations of convex bodies, random matrices, related methods in discrete mathematics or questions of complexity. The program is available now .

4. Department Of Mathematics - University Of Idaho
convex geometry and Discrete Optimization. Mark Nielsen (also see the web page on Dr. Nielsen s research interests).
http://www.uidaho.edu/math/research/geometry.htm

5. Dept. Of Math -Research - Mathematical Biology
convex geometry and Discrete Optimization. Mark Nielsen.
http://www.uidaho.edu/LS/Math/research/geometry.htm

6. Recent Publications, Gideon Schechtman
convex geometry and Local Theory of Normed Spaces. An ``isomorphic version of Dvoretzky s theorem (with VD Milman), CR Acad. Sci.
http://www.wisdom.weizmann.ac.il/mathusers/gideon/pubsTopics/recentPubsByTopicLo

Extractions: Convex Geometry and Local Theory of Normed Spaces An ``isomorphic" version of Dvoretzky's theorem (with V.D. Milman Global vs. local asymptotic theories of finite dimensional normed spaces (with V.D. Milman ), Duke Math. J. 90 (1997), 7393. An ``isomorphic" version of Dvoretzky's theorem II (with V.D. Milman ), Convex geometric analysis (Berkeley, CA, 1996), Math. Sci. Res. Inst. Publ., 34, Cambridge Univ. Press, Cambridge, (1999). Averages of norms and behavior of families of projective caps on the sphere (with A.E. Litvak and V.D. Milman Averages of norms and quasi-norms (with A.E. Litvak and V.D. Milman ), Math. Annalen 312 (1998), 95124. (with A. Zvavitch ), Math. Nachr. 227 (2001), 133142. Concentration, results and applications , in preparation for handbook, preliminary version available. Finite dimensional subspaces of \$L_p\$ (with W.B. Johnson ), Handbook of the Geometry of Banach Spaces, Vol 1, W.B. Johnson and J. Lindenstrauss, eds, Elsevier, Amsterdam (2001), 837870. (with J. Zinn

7. Abteilung Für Analysis - Research
Main research. convex geometry, In convex geometry, geometric and analytic methods are used to study convex sets and convex functions.
http://dmg.tuwien.ac.at/fg6/research.html

Extractions: Geometry of Numbers Geometry of Numbers forms a bridge between convexity, Diophantine approximation and the theory of quadratic forms. Today it is an independent problem-oriented field of mathematics having relations with coding theory, numerical integration, computational geometry and optimization. Geometry of Numbers has a long tradition in Vienna and at the Department of Analysis the following problems are studied: TU Wien Deutsche Version Homepage

8. Foundations Of Convex Geometry
Home Catalogue Foundations of convex geometry. Foundations of convex geometry. WA Coppel. Published March 1998. 236 pages. Paperback ISBN 0521639700.
http://books.cambridge.org/catalogue.asp?isbn=0521639700

9. CMIS Research - Image Analysis - Applications/Work Overview - Hyperspectral Imag
scene). Fig. 2 Toy example of convex geometry model (M = 3) with noise endmembers lie at the vertices of the triangle. The leading
http://www.cmis.csiro.au/iap/RecentProjects/hyspec_eg.htm

Extractions: Fig. 1: (a) 54 AVIRIS shortwave infrared images of Oatman, Arizona (courtesy of NASA JPL). (b) "Stackplot" of spectra at 6 pixels in the Oatman Image. Please click on the images for an enlarged view. Fig. 2: Toy example of convex geometry model (M = 3) with noise: endmembers lie at the vertices of the triangle The leading hyperspectral image analysis package, ENVI , has a method which finds the "pointiest" pixels (i.e. near vertices) using the "Pixel Purity Index". Clusters of such points are identified interactively as likely endmember clusters. More sophisticated methods include those of Craig (1994) which finds the simplex of minimum volume with a given number of vertices and completely enclosing the data "cloud"; and the N-FINDR algorithm of Winter (1999), which finds the simplex of maximum volume whose vertices are constrained to be a subset of the data points. N-FINDR is in commercial use. The Craig and Winter solutions for the toy example are shown in Fig. 3 (in pink and blue respectively). Note that Craig's solution is too large in the presence of noise, while Winter's will be too small if some materials in the scene are not represented by whole pixels.

10. Polytechnic University Department Of Mathematics: Instructional Team
Erwin Lutwak Ph.D., Polytechnic Institute of Brooklyn convex geometry, geometric and analytic inequalities Phone (718) 2603366 Email elutwak@poly.edu Office
http://www.math.poly.edu/people/instructional_team.phtml

But, if we think of the great advances in convex geometry, the calculus of variations, integral geometry, the theory of metric spaces, and symplectic geometry
http://www.math.poly.edu/research/finsler/

Extractions: The Finsler Geometry Newsletter EDITORIAL PAGE AUTHOR INDEX INTRODUCTION PREPRINTS ... LINKS Created: Nov 18, 1999 Last update: Welcome to the Finsler Geometry Newsletter. The aim of the Newsletter is to promote the interaction between researchers in convex, integral, metric, and symplectic geometry by providing them with a quick, accessible medium for communicating ideas, announcements, examples, counter-examples, and remarks. Criticisms and comments should be addressed to the webmaster The webmaster: Juan Carlos Alvarez Volumes in normed and Finsler spaces by Serge Tabachnikov Finsler manifolds, manifolds whose tangent spaces carry a norm that varies smoothly with the base point, were born prematurely in 1854 together with the Riemannian counterparts in Riemann's ground-breaking Habilitationsvortrag . I say prematurely because in 1854 Minkowski's work on normed spaces and convex bodies was still forty three years away, and thus not even the infinitesimal geometry on which Finsler manifolds are based was understood at the time. Apparently, Riemann did not know what to make of these 'more general class' of manifolds whose element of arc-length does not originate from a scalar product and, fatefully, put in a bad word for them:

12. Wlodek's Geometry Papers
with convex sets, Chapter 3.3, vol. B, in Handbook of convex geometry, P. Gruber and J. Wills, Eds., NorthHolland 1993, 799-860.
http://www.auburn.edu/~kuperwl/geometry.html

13. Convolution Inequalities In Convex Geometry
Thematic Programme on Aymptotic Geometric Analysis Conference on Convexity and Asymptotic Theory of Normed Spaces. Convolution Inequalities in convex geometry.
http://www.pims.math.ca/science/2002/aga/convexityvideos/ball/

14. AMS-UMI 2002 : Special Sessions
4) Analytic Aspects of convex geometry S. Campi (University of Modena) campi@unimo.it R. Gardner (Western Washington University) Richard.Gardner@wwu.edu E
http://www.dm.unipi.it/~meet2002/italiano/session04.html

15. Introduction
Convex is a Maple package for computations in rational convex geometry. The package provides functions for linear as well as affine convex geometry.
http://www.mapleapps.com/powertools/convex/docs/intro.html

Extractions: Contents Convex is a Maple package for computations in rational convex geometry. Here "rational" means that all coordinates must be rational numbers. The package provides functions for "linear" as well as "affine" convex geometry. In the affine setting, the basic objects are polyhedra, which are intersections of finitely many (affine) halfspaces. Polyhedra can also be described as the convex hull of finitely many points and rays. A bounded polyhedron is also called a polytope. In the Convex package, polyhedra are represented by the type POLYHEDRON . They may contain lines and may not be full-dimensional. The most important functions to define a POLYHEDRON are POLYHEDRON[convhull] and POLYHEDRON[intersection] The linear setting is based on cones, which are intersections of finitely many linear halfspaces (i.e., whose boundary contains the origin). They are generated by finitely many rays. In the Convex package, cones are represented by the type CONE . They may contain lines and may not be full-dimensional. A CONE can be created from either description with the functions CONE[poshull] and CONE[intersection] , respectively.

16. Maple Application Center
Careers. Contact Us. Geometry, convex geometry, Solving and Displaying Inequalities, The Intersection of a Line and Cone, The Intersection of a Line and Cylinder,
http://www.mapleapps.com/List.asp?CategoryID=11&Category=Geometry

17. DISPLAY AGENDAS A0344
Opening 15 , 1415 1515, Toric ring and discrete convex geometry (1) - 1h00 , W. Bruns Universität Osnabrück, Germany. 1515 1545, Break - 30 . 1545 1645,
http://agenda2.ictp.trieste.it/cdsagenda5/full_display.php?ida=a0344

18. Geometric And Convex Combinatorics
the solution of problems in integer programming have their origin in various fields of mathematics, such as Geometry of Numbers, convex geometry, Algebra, or
http://www.math.uni-magdeburg.de/institute/imo/research/geometry_html/geometry.h

Extractions: Next: References Geometric and convex combinatorics Methods for the solution of problems in integer programming have their origin in various fields of mathematics, such as Geometry of Numbers Convex Geometry Algebra , or Number Theory . The reason for this is the fact that the study of relations between discrete structures (lattices) and continuous sets (convex bodies, cones) is of fundamental importance for all of them. In this project we are trying to utilize current methods and results from the fields mentioned above for integer programming, and to contribute to a better understanding of lattice structures in connection with convex sets. The individual projects can be classified as follows: In 1896 Minkowski laid the foundation of what is today called the Geometry of Numbers , when he solved problems in number theory using geometric methods and interpretations. Today it is an independent field of research with close ties to other mathematical disciplines, for example coding theory and integer programming.

19. Semi-infinite Optimization
Recent applications of semiinfinite optimization techniques to geometric extremal problems are opened up in the last years, first of all in convex geometry.
http://www.math.uni-magdeburg.de/institute/imo/research/semiinfinite_html/semiin

Extractions: There is a great variety of (classical) applications of semi-infinite optimization, including problems in approximation theory (with respect to polyhedral norms), operation research, optimal control, boundary value problems and others. These applications and appealing theoretical properties of semi-infinite problems gave rise to intensive (and up to now undiminished) research activities in this field since its inceptive appearing in the 1960s. Describing an n-dimensional convex body by its Minkowski support function, there occur in a very natural way systems of (infinitely many) linear inequalities with a finite number of variables. Additionally, any inclusion of two convex bodies can equivalently be formulated by the inequality for all directions , where h k are the support functions of C K , respectively. So the feasible regions of extremum problems corresponding to coverings or embeddings in convex geometry can be described by semi-infinite systems and semi-infinite optimization techniques turn out to be an appropriate tool for handling them.

20. UCL > The Department Of Mathematics > The Department
geometry of measures (as presented in Mattila Geometry of sets and measures in Euclidean spaces, Cambridge University Press 1995), convex geometry, ( see the