Banach July 2008

banach@mathdept.okstate.edu

2 participants
15 discussions

Abstract of a paper by Greg Kuperberg
by alspach＠fourier.math.okstate.edu 10 Jul '08

10 Jul '08

This is an announcement for the paper "From the Mahler conjecture to Gauss linking integrals" by Greg Kuperberg. Abstract: We establish a version of the bottleneck conjecture, which in turn implies a partial solution to the Mahler conjecture on the product $v(K) = (\Vol K)(\Vol K^\circ)$ of the volume of a symmetric convex body $K \in \R^n$ and its polar body $K^\circ$. The Mahler conjecture asserts that the Mahler volume $v(K)$ is minimized (non-uniquely) when $K$ is an $n$-cube. The bottleneck conjecture (in its least general form) asserts that the volume of a certain domain $K^\diamond \subseteq K \times K^\circ$ is minimized when $K$ is an ellipsoid. It implies the Mahler conjecture up to a factor of $(\pi/4)^n \gamma_n$, where $\gamma_n$ is a monotonic factor that begins at $4/\pi$ and converges to $\sqrt{2}$. This strengthens a result of Bourgain and Milman, who showed that there is a constant $c$ such that the Mahler conjecture is true up to a factor of $c^n$. The proof uses a version of the Gauss linking integral to obtain a constant lower bound on $\Vol K^\diamond$, with equality when $K$ is an ellipsoid. It applies to a more general conjecture concerning the join of any two necks of the pseudospheres of an indefinite inner product space. Because the calculations are similar, we will also analyze traditional Gauss linking integrals in the sphere $S^{n-1}$ and in hyperbolic space $H^{n-1}$. Archive classification: math.MG math.DG math.FA Remarks: 10 pages, 4 figures. Dedicated to my father, on no particular The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math/0610904 or http://arXiv.org/abs/math/0610904 or by email in unzipped form by transmitting an empty message with subject line uget math/0610904 or in gzipped form by using subject line get math/0610904 to: math(a)arXiv.org.

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SUMIRFAS-2nd announcement
by Bill Johnson 10 Jul '08

10 Jul '08

2nd ANNOUNCEMENT OF SUMIRFAS 2008 The Informal Regional Functional Analysis Seminar August 8 - 10 Texas A&M University, College Station Confirmed speakers and titles are given below. The schedule for SUMIRFAS will be posted on the Workshop in Analysis and Probability page, URL http://www.math.tamu.edu/research/workshops/linanalysis/ The first talk will be in the early afternoon on Friday and the Seminar concludes by lunch time on Sunday. All talks will be in Blocker 165. The Blocker Building is on Ireland St. just south of University Dr. on the Texas A&M campus: http://www.tamu.edu/map/building/overview/BLOC.html. Coffee and refreshments will be available in Blocker 155. Julien Giol <giol(a)math.tamu.edu>, David Kerr (chair) <kerr(a)math.tamu.edu>, and Andrew Toms <atoms(a)mathstat.yorku.ca> are organizing a Concentration Week on "Operator Algebras, Dynamics, and Classification" which will take place August 4-8. For more information, go to http://www.math.tamu.edu/~kerr/concweek08.html. Ron Douglas <rdouglas(a)math.tamu.edu> and Jaydeb Sarkar <jsarkar(a)math.tamu.edu> are organizing a Concentration Week on "Multivariate Operator Theory" that will take place July 28 - August 1. For more information, please visit URL http://www.math.tamu.edu/~jsarkar/cowmot.html. On Saturday evening there will be a BBQ at the home of Jan and Bill Johnson. We expect to be able to cover housing for most participants from support the National Science Foundation has provided for the Workshop. Preference will be given to participants who do not have other sources of support, such as sponsored research grants. When you ask Cara to book your room, please tell them if you are requesting support. Minorities, women, graduate students, and young researchers are especially encouraged to apply. For logistical support, please contact Cara Barton, cara(a)math.tamu.edu. For more information on the Workshop itself, please contact William Johnson, johnson(a)math.tamu.edu, David Larson, larson(a)math.tamu.edu, Gilles Pisier, pisier(a)math.tamu.edu, or Joel Zinn, jzinn(a)math.tamu.edu. Speakers include: Bill Arveson, Maximal vectors in Hilbert space and quantum entanglement Nate Brown, Hilbert modules and the Cuntz semigroup Marius Dadarlat, Finite dimensional approximations of amenable groups Ron DeVore, A Taste of Compressed Sensing Detelin Dosev, Commutators on certain Banach spaces Constanze Liaw, Singular integrals and rank one perturbations Timur Oikhberg, The complexity of the complete isomorphism relation between subspaces of an operator space (joint work with C. Rosendal) Grigoris Paouris, Small ball probability estimates for log-concave measures Chris Phillips, Freeness of actions of finite groups on C*-algebras Bunyamin Sari, On uniform classification of the direct sums of $\ell_p$-spaces Nicole Tomczak-Jaegermann, Random embeddings and other high-dimensional geometric phenomena Elisabeth Werner, Orlicz functions and minima and maxima of random variables

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Abstract of a paper by Konrad J. Swanepoel
by alspach＠fourier.math.okstate.edu 01 Jul '08

01 Jul '08

This is an announcement for the paper "Simultaneous packing and covering in sequence spaces" by Konrad J. Swanepoel. Abstract: We adapt a construction of Klee (1981) to find a packing of unit balls in $\ell_p$ ($1\leq p<\infty$) which is efficient in the sense that enlarging the radius of each ball to any $R>2^{1-1/p}$ covers the whole space. We show that the value $2^{1-1/p}$ is optimal. Archive classification: math.MG math.FA Mathematics Subject Classification: 46B20 (primary), 52C17 (secondary) Remarks: 5 pages The source file(s), klee.tex: 14156 bytes, is(are) stored in gzipped form as 0806.4473.gz with size 5kb. The corresponding postcript file has gzipped size 92kb. Submitted from: konrad.swanepoel(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0806.4473 or http://arXiv.org/abs/0806.4473 or by email in unzipped form by transmitting an empty message with subject line uget 0806.4473 or in gzipped form by using subject line get 0806.4473 to: math(a)arXiv.org.

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Abstract of a paper by Joel A. Tropp
by alspach＠fourier.math.okstate.edu 01 Jul '08

01 Jul '08

This is an announcement for the paper "Column subset selection, matrix factorization, and eigenvalue optimization" by Joel A. Tropp. Abstract: Given a fixed matrix, the problem of column subset selection requests a column submatrix that has favorable spectral properties. Most research from the algorithms and numerical linear algebra communities focuses on a variant called rank-revealing {\sf QR}, which seeks a well-conditioned collection of columns that spans the (numerical) range of the matrix. The functional analysis literature contains another strand of work on column selection whose algorithmic implications have not been explored. In particular, a celebrated result of Bourgain and Tzafriri demonstrates that each matrix with normalized columns contains a large column submatrix that is exceptionally well conditioned. Unfortunately, standard proofs of this result cannot be regarded as algorithmic. This paper presents a randomized, polynomial-time algorithm that produces the submatrix promised by Bourgain and Tzafriri. The method involves random sampling of columns, followed by a matrix factorization that exposes the well-conditioned subset of columns. This factorization, which is due to Grothendieck, is regarded as a central tool in modern functional analysis. The primary novelty in this work is an algorithm, based on eigenvalue minimization, for constructing the Grothendieck factorization. These ideas also result in a novel approximation algorithm for the $(\infty, 1)$ norm of a matrix, which is generally {\sf NP}-hard to compute exactly. As an added bonus, this work reveals a surprising connection between matrix factorization and the famous {\sc maxcut} semidefinite program. Archive classification: math.NA math.FA Mathematics Subject Classification: 15A60; 15A23; 65F30; 90C25 Remarks: Conference version The source file(s), alg.sty: 7607 bytes macro-file.tex: 8456 bytes subset-selection-soda-v4.bbl: 4536 bytes subset-selection-soda-v4.tex: 88398 bytes, is(are) stored in gzipped %form as 0806.4404.tar.gz with size 30kb. The corresponding postcript file has gzipped size 109kb. Submitted from: jtropp(a)acm.caltech.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0806.4404 or http://arXiv.org/abs/0806.4404 or by email in unzipped form by transmitting an empty message with subject line uget 0806.4404 or in gzipped form by using subject line get 0806.4404 to: math(a)arXiv.org.

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Abstract of a paper by Pascal Lefevre, Daniel Li, Herve Queffelec, and Luis Rodriguez-Piazzaa
by alspach＠fourier.math.okstate.edu 01 Jul '08

01 Jul '08

This is an announcement for the paper "A criterion of weak compactness for operators on subspaces of Orlicz spaces" by Pascal Lefevre, Daniel Li, Herve Queffelec, and Luis Rodriguez-Piazzaa. Abstract: To appear in J. Funct. Spaces and Appl. Archive classification: math.FA Mathematics Subject Classification: 46E30 Remarks: 18 pages The source file(s), critere.tex: 40456 bytes, is(are) stored in gzipped form as 0806.4204.gz with size 13kb. The corresponding postcript file has gzipped size 97kb. Submitted from: lefevre(a)euler.univ-artois.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0806.4204 or http://arXiv.org/abs/0806.4204 or by email in unzipped form by transmitting an empty message with subject line uget 0806.4204 or in gzipped form by using subject line get 0806.4204 to: math(a)arXiv.org.

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Banach July 2008