-
Wednesday, February 13, 3pm, room CAB 457.
Speaker: Sandra Pott (University of Glasgow)
Title:
Tangential interpolation in vector-valued spaces and
application to controllability.
Abstract:
click here.
-
Tuesday, February 12, 3:30pm, room CAB 357.
Speaker: Marina Yaskina (University of Oklahoma)
Title:
Intersection bodies and Lp-spaces.
Abstract:
What is an intersection body? Do there exist non-intersection bodies all of
whose central sections are intersection bodies? What is the relation
between intersection bodies and Lp spaces with p<0?
What is the notion of a normed spaces being embedded in L0?
In this talk we will give an answer to these and some other related
-
Colloquium:
Thursday, January 10, 3:30pm, room CAB 657
Speaker: Vitali Milman (Tel Aviv University)
Title:
symptotic Geometric Analysis: The Concept of Polarity and Geometrization of
Probability
Abstract:
The Asymptotic Geometric Analysis studies the asymptotic behavior of
finite- (but very high-)dimensional normed spaces and convex bodies
when dimension tends to infinity. Contrary to common intuition, which
anticipates enormous diversity and chaotic behavior, we observe a
uniform behavior for the whole family of finite- (but
high-)dimensional spaces. In the Introduction to our talk we will
demonstrate a couple of different and unexpected phenomena
accompanying high dimension. In the second, the main part of the talk
we will explain how the geometric theory of convexity is extended to a
larger category of log-concave measures which bring inside this class
of (probability) measures geometric vision and approach. In
particular, this point of view introduces functional versions for many
geometric inequalities, and also leads to solutions of some central
problems of the theory. It also leads to the discovery of the
abstract notion of Duality (Polarity) with many unexpected results
outside the particular field we discuss.
-
Wednesday, January 9, 3pm, CAB 657.
Speaker: Sergey Bobkov (Univ of Minnesota)
Title:
Weighted Poincare-type inequalities for convex
measures with heavy tails.
Abstract:
We will be discussing some integro-differential
inequalities with weight for probability distributions
under convexity hypotheses of the Brunn-Minkowski type. Basic examples include the family of the generalized multidimensional Cauchy measures. This is a joint work with Michel Ledoux.
Garth Dales (Leeds University) gave a colloquium and a
seminar talk.
-
Friday, November 30, 3:30pm, CAB 457
Title:
Banach algebras of continuous functions and
measures, and their second duals.
Abstract:
For every Banach algebra A, there are two products on
the second dual space A'' that make A'' into a Banach
algebra; they may or may not coincide. A lot of
information about the original algebra A comes easily
by looking at these second duals. We shall first give
the basic definitions and some (old and new)
examples.
The first detailed example is the case where A is
C_0(Omega), an algebra of continuous functions on a
locally compact space Omega.
Next, let G be a locally compact group, and
let
L1(G) and M(G) be the group algebra
and the measure
algebra on G, respectively. We shall describe the
second duals L1(G)'' and M(G)'', giving some
classical results, some new results, and some open
questions.
-
Colloquium:
Thursday, November 29, 3:30--4:30, CAB 657
Title:
Multi-Banach spaces and multi-Banach algebras.
Abstract:
The very extensive theories of Banach spaces and Banach algebras,
including algebras of operators on Banach spaces, are the foundation
stones of much modern analysis.
For certain reasons M. Polyakov and I were led to introduce a more
general notion: that of a multi-Banach space. Roughly we replace a
norm on a Banach space E by a sequence of norms on the spaces E^n.
Similarly we obtain multi-Banach algebras.
I hope to convince you that this is a useful notion by showing the
following: multi-norms give information that distinguishes Banach
spaces in an apparently new way; there are lots of examples,
especially related to Banach lattices; we generate new examples of
algebras of operators on a Banach space; we capture some notions of
amenability in a new way.
Rolf Schneider (Freiburg University),
gave two seminar talks and a colloquium talk:
-
Friday, October 26, 3:30pm, CAB 457
Title:
Sums of congruent convex bodies
Abstract:
The Minkowski linear combination is a fundamental operation for convex
bodies. Further basic structures on the space of convex bodies are the
topology induced by the Hausdorff metric, and the operation of the
group of rigid motions. Suppose we have only one convex body B at our
hands and want to produce other convex bodies from it by using just
these basic operations, that is, taking Minkowski linear combinations
of congruent copies of B, and limits. How far do we get? Not very far:
we obtain only a nowhere dense class of convex bodies (example: if B
is a segment, we obtain the zonoids). What if we allow also
subtractions', in the following sense: we say that B generates the
convex body K if K can be represented by
K+M1 = M2,
where M1 and M2
are limits of Minkowski linear combinations of congruent copies of
B. Our aim is to characterize the convex bodies B that generate a
dense class of convex bodies, and to show that they are also dense.
This involves some elementary harmonic analysis. (Joint work with
Franz Schuster.)
-
Colloquium:
Thursday, October 25, 3:30--4:30, CAB 657
Title:
Asymptotic shapes of random polytopes
Abstract:
We consider random polytopes, generated as intersections of closed
halfspaces (containing 0) bounded by the hyperplanes of a Poisson
process of hyperplanes (satisfying only some homogeneity property
under dilatations). The central question (a very general version of
D.G. Kendall's problem) asks for the asymptotic shape of the random
polytope under the condition that it is large (measured in various
ways). The answer depend on the extremal bodies of inequalities of
isoperimetric type for certain functionals of convex bodies, and
stability results for these lead to estimates for probabilities of
large deviations from asymptotic shapes. (Joint work with Daniel Hug
and partially with Matthias Reitzner)
-
Educational talk for graduate students:
Tuesday, October 23, 1pm, CAB 657
Title:
Random projections of regular polytopes and neighborliness
Abstract:
If an N-dimensional regular crosspolytope is projected to a uniform
random d-dimensional subspace and N is large, then the projection has
strong neighborliness properties, with high probability. Strong
results in this direction were recently obtained by David Donoho. I
plan to explain the geometric background (without analytic details).
-
Tuesday, October 16, 1pm, CAB 657
Speaker: Alexander Koldobsky
(University of Missouri-Columbia)
Title:
The complex Busemann-Petty problem on sections of convex bodies.
Abstract:
TBA
2006-2007
-
Wednesday, June 20, 10am, CAB 657
Speaker: Matt Daws
(St John's College, Oxford)
Title: Contractability of algebras of
operators
Abstract:
Contractability is a very strong homological condition which can be
put on an algebra. In the algebraic case, it is equivalent to being
finite dimensional and of a very simple form. This also holds in the
topological case, at least for C*-algebras. In this talk I will talk
about how things fail to work so well if we consider the algebra of
operators on a Banach space. Our methods are elementary and should be
easy to follow, but surprisingly seem to recover almost all known
results.
-
Friday, March 23, 3pm, CAB 657
Speaker: John Pym
(University of Sheffield)
Title: Minimal determinants for the centres
and topological centres of some group compactifications.
Abstract:
The algebraic centre of the uniformly continuous compactification
GUC of an abelian locally compact group G is
G itself. There is a stronger result: if u commutes with
just two (carefully chosen) elements of GUC then
u must be in G. The topological version of this idea is
that if uvj -> uv whenever vj -> v
in GUC, then u is in G. In fact just
one convergent net is absolutely necessary. Easy proofs of these
facts will be given.
-
Friday, March 16, 3pm, CAB 657
Speaker: Yevgeniy Gordon
(Eastern Illinois University)
Title: Mathematics in a hyperfinite world
Abstract
-
Wednesday, March 14, 3pm, CAB 365
Speaker: Eberhard Kaniuth
(University of Paderborn)
Title:
Hardy's Uncertainty Principle for Lie Groups
Abstract:
A classical theorem due to Hardy says that a non-zero measurable
function on the real line and its Fourier transform cannot both have
very strong exponential decay. Hardy's theorem also holds for
Rn, and
during the past ten years there has been much effort to prove
Hardy-like theorems for various classes of connected Lie
groups. Specifically, analogues of Hardy's theorem have been
established for motion groups, non-compact connected semisimple Lie
groups with finite centre and simply connected nilpotent Lie
groups. The talk will survey these results and finally focus on recent
work on non-simply connected nilpotent Lie groups.
-
Friday, Feb 16, 3pm, CAB 657
Speaker: Shahar Mendelson
(Technion, Haifa and Australian National University, Canberra)
Title: Subgaussian processes are well-balanced.
Abstract
-
Tuesday, Jan 16, 2:00pm, room CAB 281
Speaker: Isaac Namioka (Univ of Washington)
Title: Distance to spaces of Baire-1 functions.
Abstract:
This talk is a joint work with Bernardo Cascales and his student
Carlos Angosto. The theme of our research is to give qualitative
versions of some well-known theorems in functional analysis. To
illustrate this I describe one such result. First some notation. Let X
be a topological space and (Z,d) be a metric space. Then C(X,Z)
denotes the space of all continuous maps from X into Z. A map f:X--> Z
is called a Baire-1 (Z-valued) function (or, map) if it is the
pointwise limit of a sequence in C(X,Z). We denote the set of all such
maps by B1(X,Z).
In 1993, Srivatsa published the following surprisingly strong result:
Let f be a map from a metric space Z into a Banach space E. If f:
Z-->(E, weak) is continuous then f is in B1(Z,(E,norm)).
Our qualitative version of this theorem goes as follows: Let f :
Z-->(E**, weak*) be continuous. Then d(f,B1(Z,E)) \le (3/2)
sup{ osc f(z) : z in Z }, where f(z) is considered a real-valued
function on (BE*, weak*). Recall that for a real-valued
function h on a topological space T and t in T,
osc(h,t)=inf{ diam
h(U) : U a neighborhood of t }
and
osc(h) = sup{ osc(h,t) : t
in T }.
Srivatsa's theorem corresponds to the case where
osc(h(z))=0 for each z in Z. I hope to be able to present two or
three additional instances of such qualitative versions.
-
Tuesday, Dec 5, 3:30pm CAB 377
Speaker: Pedro Tradacete (Univ Complutense Madrid)
Title: Strictly singular operators on Banach
lattices.
-
Wednesday Nov 15, 2:00pm, CAB 269
Speaker: Apostolos Giannopoulos (Univ of Athens)
Title: Distribution of volume on convex
bodies.
-
Tuesday, Nov 7, 3:30pm, CAB 377
Speaker: Sergey Tikhonov
Title: "Good" and "bad" series in classical harmonic analysis Abstract.
-
Tuesday, October 24, 3:30pm, CAB 365
Speaker: Andriy Prymak, University of Alberta.
Title: Convex multivariate approximation by
algebras of continuous functions.
-
Tuesday, October 17, 3:30pm, CAB 365
Speaker: Jean Ludwig, Universite de Metz.
Title: Primary ideals in the group algebra of nilpotent Lie groups.
-
Series of three talks by Hermann Koenig, a distinguished
visitor of PIMS.
Speaker: Hermann Koenig, Universitaet Kiel.
Title: Brascamp-Lieb inequality.
Abstract
Dates:
- September 6 at 11am, CAB 457
- September 13 at 4:30pm, CAB 657
- September 18 at 4:30pm, CAB 657
-
Friday, August 18, 2pm-3:30pm, CAB 657 and
Tuesday, August 22, 2pm-3pm, room 657
Speaker: Yehoram Gordon, Technion - Israel Institute of Technology.
Title: Geometrical applications of the
Gaussian min-max theorem.
2005-2006
-
Monday, March 27, 12-1pm, CAB 657
Speaker: Thomas Schlumprecht, Texas A&M University.
Title: Embeddings into Banach spaces with finite dimensional
decompositions.
Abstract:
We consider the following general problem: Given a class C of
Banach spaces, is there an element of C, or in a class,
closely related to C, which is universal for the class C,
meaning that every member of C is isomorphically a subspace
of X? In many cases these type questions can be easily solved in
the category of spaces having a basis, or more generally, a finite
dimensional decomposition (FDD). Then, the aforementioned problem
becomes a problem of the following type: Can a Banach space X in
certain class C be embedded into a space Z of that class, or
to a class closely related to C, with Z having
a basis or an FDD?
In our talk we will present a general combinatorial argument leading
to the solutions of these type of problems. Secondly, we present the
solution some concrete problems using our machinery:
- Intrinsic characterization of subspaces of lp-sums
of finite dimensional subspaces (Question by W.B. Johnson in
1977).
- Existence of a separable reflexive Banach space containing
all separable super reflexive Banach spaces (Question
by J.Bourgain in 1980).
- Existence of separable reflexive spaces being universal
for the class of separable reflexive spaces with given
Szlenk index (Problem by A.Pełczyński 2005)
The work presented is joint work with E.Odell (for (1) and (2)),
and joint work with E.Odell and A.Zsák (for (3))
- Monday, March 20, 12:05-1pm, CAB 657
Speaker: Alexander Litvak, University of Alberta.
Title: On the vertex index of convex
bodies, (joint work with K. Bezdek)
Abstract:
We introduce the vertex index of a given d-dimensional
centrally symmetric convex body, which, in a sense, measures how well
the body can be inscribed into a convex polytope with small number of
vertices. This index is closely connected to the illumination
parameter of a body, introduced earlier by Karoly Bezdek, and, thus,
related to the famous conjecture in Convex Geometry about covering of
a d-dimensional body by 2d smaller positively
homothetic copies. We provide asymptotically sharp (up to logarithmic
terms) estimates of this index in the general case and discuss
extremal cases. More precisely, we show that the vertex index varies
between cd/(ln 2d)1/2 and
Cd3/2ln(2d), where c and
C are absolute positive constants. Here, the lower estimate is sharp
(up to a logarithmic term) for crosspolytopes and the upper estimate
is sharp (again, up to a logarithmic term) for ellipsoids. Also, we
provide precise estimates in dimensions 2 and 3. We conjecture that
the vertex index of a d-dimensional Euclidean ball is
2d3/2. We prove this conjecture in dimensions two and three.
-
Friday, March 17, 12:05-1pm, CAB 657
Speaker: Alexander Kiselev, University of Wisconsin.
Title: Quantum scattering and almost
everywhere convergence of linear operators
Abstract:
We review recent results on scattering and spectrum of Schroedinger
operators with slowly decaying potentials. If the potential is in
Lp(R) with p<2, we prove
existence of wave operators and eigenfunctions with plane wave
WKB-type asymptotic behavior. The proofs employ methods of Fourier
analysis, in particular results on almost everywhere convergence for a
class of multilinear operators. The borderline case of potential from
Lp(R) is still open, and can be viewed
as a nonlinear version of the celebrated Carleson theorem on the
almost everywhere convergence of Fourier series of an
L2 function.
-
Friday, March 10, 12-1pm, CAB 657
Speaker: Alexander Koldobsky, University of
Missouri-Columbia.
Title: Khinchin type inequalities and
sections of Lp-balls
Abstract:
We extend Khinchin type inequalities to the case
p>-2 and apply this to verify the slicing problem for the
unit balls of finite-dimensional spaces that embed in
Lp, p>-2.
-
Friday, November 25, 3:30, room: CAB 563
Speaker: Arkady Kitover, Community College of
Philadelphia.
Title: Invariant Subspaces of Positive Operators
Abstract
-
Tuesday, November 1, 3:30pm., room: CAB 377.
Speaker: Vladimir Pestov, University of Ottawa;
Title: Geometry, dynamics, and combinatorics of infinite-dimensional
groups of transformations
Abstract:
We will give a survey of some recent developments linking the
dynamical properties of "infinite-dimensional" groups of transformations
of various structures (groups of operators, of homeomorphisms, of
measure-preserving transformations, of isometries etc.) with geometry of
high-dimensional structures (asymptotic geometric analysis) and
combinatorics (Ramsey-type theorems). This new theory has its origins in
geomtric functional analysis (Dvoretzky theorem and its subsequent
analysis by V. Milman), but nowadays the examples are drawn from a number
of different areas of mathematics, one of the most important being logic
(Fraïssé theory). We will mention the remarkable Urysohn metric space, and
discuss the distortion problem versus oscillation stability in the general
context of groups of transformations.
The talk will be largely a survey of a book by the speaker recently
published in Brazil, whose text is still available on-line:
http://aix1.uottawa.ca/~vpest283/textes/rtp-impa.pdf
-
Tuesday, October 25, 3:30pm., room: CAB 377.
Speaker: Heydar Radjavi, University of Waterloo.
Title: Approximate Versions of Conditions for Simultaneous
Reducibility of Operators
Abstract:
There are known spectral conditions yielding
simultaneous invariant subspaces for collections of
operators. For example, Guralnick's theorem implies
that if S is a semigroup of complex matrices such that
AB - BA is nilpotent for every A and B in S, then S is
simultaneously triangularizable (and, in particular,
abelian if S is a compact group). An extension of this
result is also known for semigropups of compact operators
on a Banach space. Other known conditions resulting in
the same conclusion include permutability of trace (that
is, the assumption that ABC and ACB have the same trace for
every A, B, and C in the semigroup). Recently there has been
work done by several people, on approximate versions of
these conditions. For example, one can ask: what if we
assume merely that AB - BA has small spectral radius for
a semigroup of operators? The same question can be asked
with tr(ABC - ACB) assumed small. We'll talk about some
answers.
-
Tuesday, October 18, 3:30pm., room: CAB 377.
Speaker: Alexander Litvak, University of Alberta.
Title: Diameters of Sections of Convex Bodies
Abstract: (joint work with A. Pajor and N. Tomczak-Jaegermann)
We discuss the behaviour of diameters of "random" sections of convex
bodies in RN. We show that if a symmetric
convex body K in RN has ONE well
bounded k-codimensional section, then for any m>k
"random" sections of K of codimension m are also well
bounded. To prove this result we obtain a new covering lemma which is
of independent interest.
-
Tuesday, October 4, 3:30pm., room: CAB 377.
Speaker: Valentina Galvani, University of Alberta, Department of Economics.
Title: Options and Market Completeness, a functional analytic approach
Abstract
-
Thursday, September 8, 2pm., room: CAB 657.
Speaker: Garth Dales, University of Leeds.
Title: Multi-Banach algebras (joint work with M. Poliakov)
2004-2005
-
Wednesday, March 30 and April 6, 2005, 2pm, CAB 657
Speaker: Jiri Spurny, University of Alberta.
Title: Affine Baire-one functions on compact convex sets
Abstract: Let X be a compact convex subset of a locally
convex and ext X stand for the set of all extreme points of
X. We will discuss the relation between geometric properties of
X and solvability of the abstract Dirchlet problem. By this we
mean a question under what conditions we are able to extend a bounded
function f on ext X to an affine function h on
X such that h=f on ext X shares with f
prescribed toplogical properties. The lecture will be divided into
two parts. The first part will provide a survey of integral
representation theorems (Minkowski, Krein-Milman, Choquet) and facts
on infinite dimensional simplices. A connection with the potential
analysis will be established. The second talk will focus on the
aforementioned abstract Dirichlet problem for continuous and affine
Baire-one function on X.
-
Wednesday, March 23, 2005, 2pm, CAB 657
Speaker: Jan Rychtar, University of North Carolina (Greensboro).
Title: Lipschitz separated spaces and James Tree space
Abstract: Borwein, Giles and Vanderwerff investigated a class
of so called Lipschitz separated Banach spaces. Those are spaces
X where, roughly speaking, a Lipschitz function from a convex
subset C of X can be extended onto the Lipschitz
function on X in a lot of ways. They conjectured that every
such space needs to be an Asplund space (i.e. every separable space
needs to have a separable dual). In this talk, it will be shown that
a Banach space is Lipschitz separated if a certain convexity condition
of a norm is satisfied. We show as well that a James tree space
posses such a norm, and thus James Tree space is a Lipschitz separated
non-Asplund space.
-
Monday, March 14, 2005, 1pm. Room: CAB 365
Speaker: Evgene Abakumov, Université de Marne-la-Vallée.
Title: Approximation ability of lacunary and random power series.
Abstract:
We present some results concerning approximation by Taylor
remainders of lacunary and random power series. Applications to
shift-invariant subspaces and pseudoanalytic continuation will be
discussed.
-
March 9, 2005
Speaker: Adi Tcaciuc, University of Alberta.
Title: Stabilization and asymptotic structure of Banach spaces
Abstract:
The asymptotic theory of infinite dimensional Banach spaces, developed
by Maurey, Milman and Tomczak-Jaegermann, is concerned with the
structure of infinite dimensional Banach spaces manifested in the
finite-dimensional subspaces that appear everywhere far away in the
space. The class of spaces that have a simple asymptotic structure, in
the sense that we can find a 1≤p≤∞ such that all such
finite-dimensional subspaces as before are essentially
lpn's, are of
special interest and they are called asymptotic-lp spaces.
We prove that if a Banach space is saturated with infinite
dimensional subspaces in which all special n-tuples of vectors are
equivalent, uniformly in n, then the space contains
asymptotic-lp
subspaces, for some 1≤p≤∞. The proof reflects a
technique used by Maurey in the context of unconditional basic sequence
problem and extends a result by Figiel, Frankiewicz, Komorowski and
Ryll-Nardzewski.
-
February 9, 2005
Speaker: Alain Pajor, Paris VI.
Title: Diameters of Sections and Coverings of Convex Bodies.
Abstract:
We discuss some properties of entropies and coverings of symmetric
convex bodies in
Rn
from the functional analysis point of view. We
illustrate their role by a recent
seemingly counter-intuitive result that if a symmetric convex body K
in Rn has one well bounded section (in sense of the Euclidean norm)
of codimension k, then for any m>k, "random" sections of K of
codimension m are also well bounded, where randomness is meant in
sense of the Haar measure on the Grassman manifold of all
n-m-dimensional subspaces of
Rn,
and the notion of "well-bounded"
is of course properly quantified, and n is large.
-
Working Functional Analysis Seminar
Wednesday, January 26 and February 2, 2pm
Speaker: Vladimir Troitsky, University of Alberta
I will present Gleb Sirotkin's modification of Charles Read's example
of an operator on l1 with no invariant subspaces.
-
December 10, 2004, 1pm, CAB 657
Gleb Sirotkin, Northern Illinois University
Title: A simpler transitive operator
Abstract:
In 1976 P.Enflo presented the first example of a bounded operator
on a Banach space without non-trivial invariant subspaces. It was a
negative answer to the long standing open question also known as the
Invariant Subspace Problem. Subsequently, C.J.Read presented an
example of a bounded operator on l1 without non-trivial
invariant subspaces. Nevertheless, for various important classes of
Banach spaces and operators the Invariant Subspace Problem remains
unsettled.
In this talk we will see a family of operators without invariant
subspaces based on the example of C.J.Read.
We will also discuss what happens if an operator from this family
is transformed into an adjoint operator.
-
Working Functional Analysis Seminar
Wednesday, December 8, 3:00 -- 4:20 pm, CAB 373
Speaker: Volker Runde, University of Alberta
Volker Runde will present the proof of N.Ozawa on the non-amenability
of L(Lp) for p=1,2, and infinity.
-
Special seminar meeting: Working Seminar in Asymptotic Geometric Analysis
Friday, November 19, 3:00 -- 4:20 pm
Speaker: Yaozhong Hu, University of Kansas
Title: Between log-Sobolev and Spectral Gap inequalities.
Room: CAB 373
This is the continuation of Dr Hu's talk of November 5.
-
Wednesday, November 10, 2004. 3-4pm, CAB 373
Yong Zhang, University of Manitoba
Title: Approximately amenable and pseudo-amenable Banach algebras.
Abstract: Amenability is an important theory in Banach algebras. But it is also
a very restricted condition on a Banach algebra. There are basically two
different ways to generalize the notion of amenability. We will discuss
properties of these generalizations and will deal with relations between
different generalized notions of amenability.
-
Special seminar meeting: Working Seminar in Asymptotic Geometric Analysis
Friday, November 5, 3:00 -- 4:20 pm, CAB 365
Speaker: Yaozhong Hu, University of Kansas
Title: Between log-Sobolev and Spectral Gap inequalities
The lecture will expand one of the topics discussed in Yaozhong Hu's
colloquium talk and it would assume only a very basic knowledge of
probability.
-
October 13, 2004,
Ali-Amir Husain, University of Alberta
Title:On the Cohomology of Joins of Operator Algebras
Abstract:
Kraus and Schack examined finite dimensional CSL-algebras and the partially
ordered set of their minimal core projections. In unpublished work, they
proved that the Hochschild cohomology of the CSL-algebra is isomorphic to
the simplicial cohomology of a simplicial complex constructed from the core
projections.
Gilfeather and Smith used the work of Kraus and Schack to create analogues
of constructions in topology for operator algebras. They defined the notions
of cone, suspension, and join for operator algebras. Additionally, they
calculated the cohomology for cones and suspension and demonstrated that the
cohomology groups behaved exactly as the cohomology for cones and
suspensions of topological spaces. In subsequent work, the cohomology of the
join of a finite dimensional operator algebra and an arbitrary operator
algebra was calculated.
In the talk an infinite dimensional generalization of the work of Gilfeather
and Smith will be presented.
-
October 7, 2004, 11:00 - 12:00, CAB 457
(Please note unusual day/time)
Karoly Bezdek, University of Calgary
Title: On the contact graphs of finite unit ball packings in normed spaces
Abstract:
Putting it differently the talk will focus on the problem of the
maximum number of touching pairs in a finite packing of translates of a
convex body as well as on the problem of the existence of large
independent subsystems.
-
September 29, 2004. 15:00 - 16:00, CAB 457
Jiri Spurny, University of Alberta
Title: Perfect images of absolute Borel topological spaces
Abstract: A completely regular Hausdorff space X is said to be an
absolute Borel space if it is a Borel subset of any space in which X is
embedded. A characterization of such spaces will be presented as well as
their preservation with respect to perfect mappings.
The abovementioned result will be shown to follow from an easy selection
lemma which may be of some interest in itself.