(From PIMS)
NICOLE TOMCZAK-JAEGERMAN: RECIPIENT OF THE 2006 CRM-FIELDS-PIMS PRIZE
The directors of the Centre de recherches mathematiques (CRM) of
l'Universite de Montreal - Francois Lalonde, the Fields Institute -
Barbara Keyfitz, and the Pacific Institute for the Mathematical
Sciences - Ivar Ekeland, are pleased to announce the awarding of the
CRM-Fields-PIMS Prize for 2006 to Professor Nicole Tomczak-Jaegermann
of the University of Alberta in recognition of her exceptional
achievements in functional analysis and geometric analysis.
The prize was established in 1994 as the CRM-Fields prize to recognize
exceptional research in the mathematical sciences. In 2005, PIMS
became an equal partner and the name was changed to the
CRM-Fields-PIMS prize. A committee appointed by the three institutes
chooses the recipient.
Nicole Tomczak-Jaegermann, this year's recipient, is one of the
world's leading mathematicians working in functional analysis. She
has made outstanding contributions to infinite dimensional Banach
space theory, asymptotic geometric analysis, and the interaction
between these two streams of modern functional analysis.
She holds a Canada Research Chair in Geometric Analysis at the
University of Alberta. In 1998 she gave an invited lecture at the
International Congress of Mathematicians, is a Fellow of the Royal
Society of Canada, received a Killam Research Fellowship, and the
Krieger-Nelson Prize Lectureship of the Canadian Mathematical Society.
Previous recipients of the prize are H.S.M. (Donald) Coxeter, George
A. Elliott, James Arthur, Robert V. Moody, Stephen A. Cook, Israel
Michael Sigal, William T. Tutte, John B. Friedlander, John McKay,
Edwin Perkins, Donald A. Dawson, and David Boyd.
For more information please see
http://www.pims.math.ca
This is an announcement for the paper "Growth conditions and inverse
producing extensions" by Catalin Badea and Vladimir Mueller.
Abstract: We study the invertibility of Banach algebras elements
in their extensions, and invertible extensions of Banach and Hilbert
space operators with prescribed growth conditions for the norm of
inverses. As applications, the solutions of two open problems are
obtained. In the first one we give a characterization of E(T)-subscalar
operators in terms of growth conditions. In the second one we show
that operators satisfying a Beurling-type growth condition possess
Bishop's property beta. Other applications are also given.
Archive classification: Functional Analysis; Operator Algebras
Remarks: 22 pages
The source file(s), bm1arx.tex: 60879 bytes, is(are) stored in
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Submitted from: catalin.badea(a)math.univ-lille1.fr
The paper may be downloaded from the archive by web browser from
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http://front.math.ucdavis.edu/math.FA/0512321
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http://arXiv.org/abs/math.FA/0512321
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This is an announcement for the paper "Planar earthmover is not in
$L_1$" by Assaf Naor and Gideon Schechtman.
Abstract: We show that any $L_1$ embedding of the transportation
cost (a.k.a. Earthmover) metric on probability measures supported
on the grid $\{0,1,...,n\}^2\subseteq \R^2$ incurs distortion
$\Omega(\sqrt{\log n})$. We also use Fourier analytic techniques
to construct a simple $L_1$ embedding of this space which has
distortion $O(\log n)$.
Archive classification: Computational Geometry; Functional Analysis
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Submitted from: anaor(a)microsoft.com
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/cs.CG/0509074
or
http://arXiv.org/abs/cs.CG/0509074
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This is an announcement for the paper "A comment on the low-dimensional
Busemann-Petty problem" by Emanuel Milman.
Abstract: The generalized Busemann-Petty problem asks whether
centrally-symmetric convex bodies having larger volume of all
m-dimensional sections necessarily have larger volume. When m>3
this is known to be false, but the cases m=2,3 are still open. In
those cases, it is shown that when the smaller body's radial function
is a (n-m)-th root of the radial function of a convex body, the
answer to the generalized Busemann-Petty problem is positive (for
any larger star-body). Several immediate corollaries of this
observation are also discussed.
Archive classification: Functional Analysis; Metric Geometry
Remarks: 9 pages, to appear in GAFA Seminar Notes
The source file(s), low-dim-BP-problem.bbl: 4623 bytes,
low-dim-BP-problem.tex: 24305 bytes, is(are) stored in gzipped form
as 0512208.tar.gz with size 10kb. The corresponding postcript file
has gzipped size 53kb.
Submitted from: emanuel.milman(a)weizmann.ac.il
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0512208
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http://arXiv.org/abs/math.FA/0512208
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This is an announcement for the paper "Dual mixed volumes and the
slicing problem" by Emanuel Milman.
Abstract: We develop a technique using dual mixed-volumes to study
the isotropic constants of some classes of spaces. In particular,
we recover, strengthen and generalize results of Ball and Junge
concerning the isotropic constants of subspaces and quotients of
L_p and related spaces. An extension of these results to negative
values of p is also obtained, using generalized intersection-bodies.
In particular, we show that the isotropic constant of a convex body
which is contained in an intersection-body is bounded (up to a
constant) by the ratio between the latter's mean-radius and the
former's volume-radius. We also show how type or cotype 2 may be
used to easily prove inequalities on any isotropic measure.
Archive classification: Functional Analysis; Metric Geometry
Remarks: 38 pages, to appear in Advance in Mathematics
The source file(s), dual-mixed-volumes-and-slicing-problem-for-arxiv.bbl:
7985 bytes, dual-mixed-volumes-and-slicing-problem-for-arxiv.tex:
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Submitted from: emanuel.milman(a)weizmann.ac.il
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0512207
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http://arXiv.org/abs/math.FA/0512207
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Dear Friends,
In August 2006 (from the 6th to the 13th, to be precise), the Department
of Mathematical Science of Kent State University will be hosting a CBMS
conference, 'A Probabilistic and Combinatorial Approach in Analysis', with
Professor Mark Rudelson from the University of Missouri as the main
speaker. We hope that you will be able to participate.
With CBMS funding we will be able to cover local expenses for a limited
number of participants, so it is advisable to reply as soon as possible
to Artem Zvavitch (zvavitch(a)math.kent.edu). At this time, we have very
limited funding for travel; to be as efficient as possible in the use of
the available travel funds, we encourage you to encourage your graduate
students and postdocs to participate, as well.
For further information and breaking news a look at
http://www.math.kent.edu/math/CBMS.cfm
is advised.
Please note that your early response will help us gauge the needs for
housing, lecture room(s), etc. We hope to be sending out information
regarding housing by the end of December.
HOPE TO SEE YOU IN KENT NEXT AUGUST!!
Best Regards,
Richard Aron, Joe Diestel, Per Enflo, Victor Lomonosov, Andrew Tonge, and
Artem Zvavitch
This is an announcement for the paper "Generalized intersection
bodies" by Emanuel Milman.
Abstract: We study the structures of two types of generalizations
of intersection-bodies and the problem of whether they are in fact
equivalent. Intersection-bodies were introduced by Lutwak and
played a key role in the solution of the Busemann-Petty problem. A
natural geometric generalization of this problem considered by
Zhang, led him to introduce one type of generalized intersection-bodies.
A second type was introduced by Koldobsky, who studied a different
analytic generalization of this problem. Koldobsky also studied the
connection between these two types of bodies, and noted that an
equivalence between these two notions would completely settle the
unresolved cases in the generalized Busemann-Petty problem. We show
that these classes share many identical structure properties, proving
the same results using Integral Geometry techniques for Zhang's
class and Fourier transform techniques for Koldobsky's class. Using
a Functional Analytic approach, we give several surprising equivalent
formulations for the equivalence problem, which reveal a deep
connection to several fundamental problems in the Integral Geometry
of the Grassmann Manifold.
Archive classification: Functional Analysis; Geometric Topology;
Metric Geometry
Remarks: 44 pages
The source file(s), generalized-intersection-bodies-for-arxiv.bbl:
6010 bytes, generalized-intersection-bodies-for-arxiv.tex: 129282
bytes, is(are) stored in gzipped form as 0512058.tar.gz with size
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Submitted from: emanuel.milman(a)weizmann.ac.il
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/math.FA/0512058
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http://arXiv.org/abs/math.FA/0512058
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This is an announcement for the paper "Ramsey partitions and proximity
data structures" by Manor Mendel and Assaf Naor.
Abstract: This paper addresses two problems lying at the intersection
of geometric analysis and theoretical computer science: The non-linear
isomorphic Dvoretzky theorem and the design of good approximate
distance oracles for large distortion. We introduce the notion of
Ramsey partitions of a finite metric space, and show that the
existence of good Ramsey partitions implies a solution to the metric
Ramsey problem for large distortion (a.k.a. the non-linear version
of the isomorphic Dvoretzky theorem, as introduced by Bourgain,
Figiel, and Milman in \cite{BFM86}). We then proceed to construct
optimal Ramsey partitions, and use them to show that for every
$\e\in (0,1)$, any $n$-point metric space has a subset of size
$n^{1-\e}$ which embeds into Hilbert space with distortion $O(1/\e)$.
This result is best possible and improves part of the metric Ramsey
theorem of Bartal, Linial, Mendel and Naor \cite{BLMN05}, in addition
to considerably simplifying its proof. We use our new Ramsey
partitions to design the best known approximate distance oracles
when the distortion is large, closing a gap left open by Thorup and
Zwick in \cite{TZ05}. Namely, we show that for any $n$ point metric
space $X$, and $k\geq 1$, there exists an $O(k)$-approximate distance
oracle whose storage requirement is $O(n^{1+1/k})$, and whose query
time is a universal constant. We also discuss applications of Ramsey
partitions to various other geometric data structure problems, such
as the design of efficient data structures for approximate ranking.
Archive classification: Data Structures and Algorithms; Computational
Geometry; Metric Geometry; Functional Analysis
The source file(s), , is(are) stored in gzipped form as with size
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Submitted from: anaor(a)microsoft.com
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/cs.DS/0511084
or
http://arXiv.org/abs/cs.DS/0511084
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This is an announcement for the paper "On Gateaux differentiability
of pointwise Lipschitz mappings" by Jakub Duda.
Abstract: We prove that for every function $f:X\to Y$, where $X$
is a separable Banach space and $Y$ is a Banach space with RNP,
there exists a set $A\in\tilde\mcA$ such that $f$ is Gateaux
differentiable at all $x\in S(f)\setminus A$, where $S(f)$ is the
set of points where $f$ is pointwise-Lipschitz. This improves a
result of Bongiorno. As a corollary, we obtain that every $K$-monotone
function on a separable Banach space is Hadamard differentiable
outside of a set belonging to $\tilde\mcC$; this improves a result
due to Borwein and Wang. Another corollary is that if $X$ is
Asplund, $f:X\to\R$ cone monotone, $g:X\to\R$ continuous convex,
then there exists a point in $X$, where $f$ is Hadamard differentiable
and $g$ is Frechet differentiable.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46G05; 46T20
Remarks: 11 pages; added name
The source file(s), stronger_stepanoff.tex: 48652 bytes, is(are)
stored in gzipped form as 0511565.gz with size 15kb. The corresponding
postcript file has gzipped size 61kb.
Submitted from: jakub.duda(a)weizmann.ac.il
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http://front.math.ucdavis.edu/math.FA/0511565
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