Banach July 2006

banach@mathdept.okstate.edu

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SUMIRFAS schedule
by Bill Johnson 28 Jul '06

28 Jul '06

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Metric Geometry Concentration Week at A&M
by Bill Johnson 13 Jul '06

13 Jul '06

The Concentration Week on "Metric Geometry and Geometric Embeddings of Discrete Metric Spaces" will begin with registration at 9:00 AM on Monday, July 17, and end in the early afternoon on Saturday, July 22. 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. Registration and Reimbursement. Please register at the registration desk in Blocker when you arrive on Monday or Tuesday. Most participants will have their rooms direct billed to the Mathematics Department. If you are to receive a meal allowance, please fill out the reimbursement sheet given you at the registration desk with your name, social security number (if you have one), and the address to which you want the reimbursement check sent. Sign at the bottom of the form above "Traveler Signature" and check the appropriate box on that line. If you are not a U. S. resident, please give Cara your passport to be photocopied. Banquet. The Concentration Week banquet will be at 6:00 PM Thursday, July 20 at Cafe Eccell, http://www.cafeeccell.com/, 101 Church Ave. (also called Church St.), at the intersection of Church Ave. with Wellborn Road. Church Ave. is one block north of University Dr; it is an easy walk to the restaurant from Blocker. For technical reasons we must charge a registration fee of $15 per person for the banquet on Thursday, which can be paid when you register for the Concentration Week. At registration please indicate which entree (chateau loin filet, grilled chicken breast, voodoo salmon, or vegetarian) you prefer. If you will arrive after Tuesday, please email Cara, cara(a)math.tamu.edu, if you (and a companion, if applicable) will come to the banquet, because Cara must give the restaurant the number of diners in advance. Airport pick up. If you are staying at Hampton Inn, you can request a shuttle from Hampton Inn upon arrival at Easterwood Airport from the phone near the car rental desks. Alternatively, you can call the Hampton Inn at (979) 846-0184 before boarding your flight to tell them your arrival time. If you are staying elsewhere, you can ask Cara to book University Taxi. Please give Cara your arrival time and flight number. University Taxi will bill the Mathematics Department. Give the driver, usually Mr. Yimmy, your name and tell him you are attending Professor Johnson's Workshop. The 800 for University Taxi is 1-888-377-4300. Parking. You can park in the Northside Garage across the street from Blocker for $8/day if space is available. Entering and leaving the NSG is a pain and we suggest that instead you park in the Northgate Parking Garage near Church St. at 309 College Main St. for $3/day. Informal discussion. Blocker 627 and 628 can be used for informal discussions. We also have Milner 317 http://www.tamu.edu/map/building/overview/MILN.html reserved for Workshop activities, and other open rooms in Milner can be used. Computer access. Will be available in Blocker during designated hours. Please sign up at the registration desk. Also, all hotels have wireless Internet access. For security reasons TAMU does not offer wireless Internet access to visitors. Visual aids. Blocker 165 contains equipment for overhead transparency presentations, lap top attachments for power point (or the like) presentations, and white boards. Schedule. The schedule below is subject to change. We expect that "impromptu" talks will be added. Talks designed to introduce non experts and graduate students to aspects of metric geometry are mark with a *. All talks will be in Blocker 165 Note that there will be time between talks for run-over, questions, and discussion. Monday, July 17. 9:00- 9:30 Coffee, Blocker 155, & Registration in Blocker 9:30-10:20 Assaf Naor, *A survey of definitions, results and techniques in metric embedding theory, I* 10:40-11:00 Coffee and registration. 11:00-12:00 Guoliang Yu, *The Novikov conjecture and metric geometry* 12:15- 1:55 Lunch (there are a number of restaurants in the Northgate/Church Ave. area.) 1:55- 2:45 Assaf Naor, *A survey of definitions, results and techniques in metric embedding theory, II* 3:10- 4:00 Yuval Peres, Markov chains, martingales and metric embedding 4:20- Informal discussions Tuesday, July 18 9:00- Coffee, Blocker 155 9:30-10:20 Moses Charikar, *Metric Embeddings in Combinatorial Optimization* 10:45-11:45 Piotr Indyk, *Low-distortion embeddings and data structures* 12:00- 1:40 Lunch break 1:40- 2:30 Sanjeev Arora, Local versus Global phenomena and their importance in approximation algorithms 2:50- 3:15 Yury Makarychev, Directed Metrics and MIN 2CNF Deletion 3:30- 3:55 Konstantin Makarychev, Directed Metrics and Directed Graph Partitioning Problems 4:10- Informal discussions Wednesday, July 19 9:00- Coffee, Blocker 155 9:30-10:20 Bruce Kleiner, BiLipschitz embeddings of metric spaces in Banach spaces 10:40-11:10 Marianna Csornyei, Sard's theorem revisited 11:30-12:00 Leonid Kovalev, Examples of Embeddings via dynamical systems 12:20- 2:00 Lunch break 2:00- 2:50 Robert Krauthgamer, On embedding edit distance into l_1 3:10- 3:50 Yuri Rabinovich, Hard Metric from Abelian Groups 4:10- 5:00 Adi Shraibman, Margins of concept classes 5:15- Informal discussions Thursday, July 20 (Note late starting time) 9:30- Coffee, Blocker 155 10:10-11:00 Gideon Schechtman, Planar transportation cost space is not in $L_1$ 11:20-12:00 Nir Y Ailon, The Fast Johnson-Lindenstrauss Transform with Applications 12:20- 3:00 Lunch break 3:00- 3:50 James Lee, Mixed-norm embeddings and vertex isoperimetry 4:20- 5:10 Avner Magen, Integrality gaps of SDP for Vertex Cover and relations to $\ell_1$ embeddability of negative type metrics Friday, July 21 9:00- Coffee, Blocker 155 9:30-10:20 Ofer Neiman, Advances in metric embedding theory 10:40-11:30 Manor Mendel, Ramsey partitions and proximity data-structures 11:50- 1:30 Lunch break 1:30- 3:30+ Problem Session (Sanjeev Arora, moderator) 3:40- Informal discussions Saturday, July 22 9:30- Coffee, Blocker 155 10:00-10:50 Piotr Nowak, Property A 11:10-12:00 Assaf Naor, Chaining on metric spaces

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Abstract of a paper by E. Ournycheva and B. Rubin
by Dale Alspach 11 Jul '06

11 Jul '06

This is an announcement for the paper "Composite cosine transforms" by E. Ournycheva and B. Rubin. Abstract: The cosine transforms of functions on the unit sphere play an important role in convex geometry, the Banach space theory, stochastic geometry and other areas. Their higher-rank generalization to Grassmann manifolds represents an interesting mathematical object useful for applications. We introduce more general integral transforms that reveal distinctive features of higher-rank objects in full generality. We call these new transforms the composite cosine transforms, by taking into account that their kernels agree with the composite power function of the cone of positive definite symmetric matrices. We show that injectivity of the composite cosine transforms can be studied using standard tools of the Fourier analysis on matrix spaces. In the framework of this approach, we introduce associated generalized zeta integrals and give new simple proofs to the relevant functional relations. Our technique is based on application of the higher-rank Radon transform on matrix spaces. Archive classification: Functional Analysis Mathematics Subject Classification: Primary 42B10; Secondary 52A22 Remarks: 15 pages The source file(s), ctb12.tex: 51867 bytes, is(are) stored in gzipped form as 0607224.gz with size 18kb. The corresponding postcript file has gzipped size 80kb. Submitted from: ournyche(a)math.kent.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0607224 or http://arXiv.org/abs/math.FA/0607224 or by email in unzipped form by transmitting an empty message with subject line uget 0607224 or in gzipped form by using subject line get 0607224 to: math(a)arXiv.org.

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Abstract of a paper by Jorge Galindo
by Dale Alspach 10 Jul '06

10 Jul '06

This is an announcement for the paper "On unitary representability of topological groups" by Jorge Galindo. Abstract: We prove that the additive group $(E^\ast,\tau_k(E))$ of an $\mathscr{L}_\infty$-Banach space $E$, with the topology $\tau_k(E)$ of uniform convergence on compact subsets of $E$, is topologically isomorphic to a subgroup of the unitary group of some Hilbert space (is \emph{unitarily representable}). This is the same as proving that the topological group $(E^\ast,\tau_k(E))$ is uniformly homeomorphic to a subset of $\ell_2^\kappa$ for some $\kappa$. As an immediate consequence, preduals of commutative von Neumann algebras or duals of commutative $C^\ast$-algebras are unitarily representable in the topology of uniform convergence on compact subsets. The unitary representability of free locally convex spaces (and thus of free Abelian topological groups) on compact spaces, follows as well. The above facts cannot be extended to noncommutative von Neumann algebras or general Schwartz spaces. Archive classification: General Topology; Functional Analysis Mathematics Subject Classification: 43A35; 46A99; 22A10 Remarks: 11 pages The source file(s), unitfreejunio2006.tex: 39726 bytes, is(are) stored in gzipped form as 0607193.gz with size 13kb. The corresponding postcript file has gzipped size 62kb. Submitted from: jgalindo(a)mat.uji.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.GN/0607193 or http://arXiv.org/abs/math.GN/0607193 or by email in unzipped form by transmitting an empty message with subject line uget 0607193 or in gzipped form by using subject line get 0607193 to: math(a)arXiv.org.

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Banach July 2006