In alphabetical order:
(1) Bak, Jong-Guk (Korea)
Title: TBA
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(2) Barany, Imre (University College London) barany@renyi.hu
Title: On the randomized integer convex hull
Let $K\subset R^d$ be a sufficiently round convex body (the
ratio
of the circumscribed ball to the inscribed ball is bounded by
a
constant) of a sufficiently large volume. We investigate the
{\it
randomized integer convex hull} $I_L(K)=\conv(K\cap L)$, where
$L$ is a
randomly translated and rotated copy of the integer lattice
$Z^d$.
We estimate the expected number of vertices of $I_L(K)$, whose
behaviour
is similar to the expected number of vertices of the convex
hull of
$\vol K$ random points in $K$. In the planar case, we also
describe the expectation of the missed area $\vol(K\setminus
I_L(K))$.
Surprisingly, for $K$ a polygon, the behaviour in this case
is different from the convex hull of random points.
This is joint work with Jiri Matousek
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(3) Cordoba, Antonio (Universidad Autonoma de Madrid) antonio.cordoba@uam.es
Title: Fractal Fourier Series
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(4) Michael Gnewuch (University of Kiel)
Title: TBA
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(5) Grafakos, Loukas (University of Missouri at Columbia)
loukas@math.missouri.edu
Title: Sublevel set estimates for the Carleson-Hunt operator
Abstract: A certain estimate concerning the Carleson-Hunt operator
is obtained using a variation of the proof of its L^2 boundedness
given by
Lacey and Thiele via time-frequency analysis. This estimate
shown to
imply the known restricted weak type distributional estimates
of Sjolin.
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(6) Gunturk, Sinan (Courant Institute, NYU) gunturk@cims.nyu.edu
Title: One-Bit Quantization: 0-1 sequences with prescribed
moving averages
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(7) Hofmann, Steve (University of Missouri at Columbia)
hofmann@math.missouri.edu
Title: Falconer conjecture for random metrics
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(8) Kempe, Michael (Universitaet Kiel) kempe@math.uni-kiel.de
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(9) Konyagin, Sergei (Moscow State University) kon@shade.msu.ru
Title: Rearrangement of trigonometric Fourier series
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(10) Kovrizhkin, Oleg (MIT) oleg@math.mit.edu
Title: "Periodizations over integer lattices".
Abstract: We prove that if a function $f \in L^p(R^d)$
has
vanishing periodizations then $\|f\|_{p'} \le C\|f\|_{p}$,
provided $1 \le p
< \frac {2d}{d + 2}$ and dimension $d \ge 3$. We also prove
that the $L^2$-norm
ofperiodizationsof a function from $L^1(R^d)$ is equivalent
to the
$L^2(R^d)$-norm of the function itself in higher dimensions.
We generalize the
statementfor functions from $L^p(R^d)$ where $1 \le p <
\frac {2d}{d + 2}$in
the spirit of the Stein-Tomas theorem.
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(11) Magyar, Akos (University of Georgia) magyar@math.uga.edu
Title: TBA
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(12) Mockenhaupt, Gerd (Georgia Institute of Technology)
gerdm@math.gatech.edu
Title: On the Hardy-Littlewood majorant problem
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(13) Nathanson, Melvyn (City University of New York) nathansn@alpha.lehman.cuny.edu
Title: Representation functions of additive bases
for the integers
Abstract (in LaTex):
Let $A$ be a set of integers.
For every integer $n$, let $r_{A,h}(n)$ denote
the number of representations of $n$ in the form
$ n = a_1 + a_2 + \cdots + a_h,$ where $a_1,
a_2, \ldots,a_h \in A$
and $a_1 \leq a_2 \leq \cdots \leq a_h.$
The function $r_{A,h}: \Z \rightarrow \N_0\cup\{\infty\}$
is called the {\em representation function of order $h$
for $A$.}
The set $A$ is called an {\em asymptotic basis of order
$h$} if
$r_{A,h}^{-1}(0)$ is finite, that is, if every integer
with at most a finite number of exceptions can be represented
as the sum of exactly $h$ not necessarily distinct elements
of $A$.
It is proved that every function is a representation function,
that is,
if $f: \Z \rightarrow \N_0\cup\{\infty\}$ is any function
such that
$f^{-1}(0)$ is finite,
then there exists a set $A$ of integers such that $f(n)
= r_{A,h}(n)$
for all integers $n$.
Moreover, the set $A$ can be arbitrarily sparse in the
sense that,
if $\varphi(x) \rightarrow \infty$, then there exists a
set $A$
with $f(n) = r_{A,h}(n)$
such that $\card\{a\in A : |a| \leq x\} < \varphi(x)$
for all sufficiently large $x$.
If there is time in the schedule to give a second talk,
I can also present
the following:
Title: A functional equation arising from multiplication
of quantum
integers
Abstract (in LaTex):
For the quantum integer $[n]_q = 1+q+q2+\cdots + q^{n-1}$
there is a natural polynomial multiplication
such that $[m]_q\otimes_q [n]_q = [mn]_q$. This multiplication
leads
to the functional equation $f_m(q)f_n(q^m) = f_{mn}(q)$,
defined on a
given sequence
\pol\ of polynomials.
This paper contains various results concerning the construction
and classification of polynomial sequences that satisfy
the functional
equation,
as well open problems that arise from the functional equation.
\end{abstract}
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(14) Oskolkov, Konstantin (University of South Carolina)
oskolkov@math.sc.edu
Title: TBA
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(15) Sjoelin, Per (Royal Institute of Technology, Stockholm)
pers@math.kth.se
Title: A theorem of Antonov on convergence of Fourier series.
Abstract: In 1996 N.Y. Antonov proved that the Fourier series of
a function f
converges almost everywhere if f belongs to the class LlogLlogloglogL.
This
improved a result from 1968. I will discuss Antonov's proof and
some extensions
and generalizations of it. In particular I will consider differentiation
of
integrals and convergence of Walsh-Fourier series. This is joint
work with
Fernando Soria.
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(16) Solymosi, Jozsef (UCSD) solymosi@math.ucsd.edu
Title: TBA
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(17) Vega, Luis (Universidad del Pais Vasco) mtpvegol@lg.ehu.es
Title: TBA
Abstract:
... pseudodifferential calculus which appears
naturally working on Schrodinger flows
modelled on nonelliptic operators.
Title . A pseudodifferential calculus
related to nonelliptic Schrodinger equations
Abstract:
We consider variable coefficient Schrodinger flows
whose spatial operator is asymptotically closed
to the ultrahyperbolic operator $\Delta_x-Delta_y$
with $(x,y)\in $R^{n+m}$. When first order perturbations
are considered, one is naturally led
to build an integrating factor to avoid
the so called loss of derivatives obstruction.
This implies the use of a pseudodifferential
calculus introduced by Craig,
Kappeler and Strauss in the elliptic setting.
For the nonelliptic situation they impose a geometric condition
which does not hold for the symbols of interest.
In a recent work with C.E. Kenig, G. Ponce and C.Rolvung
we introduce a different class of symbols which allow
the construction of the desired integrating factor.
We plan to overview the geometric
arguments needed for the proof of the $L2$ inequality
for these pseudodifferential operators.
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(18) Wang, Yang (Georgia Institute of Technology) wang@math.gatech.edu
Title: Bernoulli convolution associated with certain non-Pisot
numbers.
Abstract: The Bernoulli convolution $\mu_\lambda$ is
the distribution of
$\sum_{n=0}^\infty \pm \lambda^n$, where the signs $\pm$ are chosen
independently with probability $1/2$ for each. It was shown by Erd\"os
that the
measure $\mu_\lambda$ is singular if $\lambda^{-1}$ is a Pisot number.
Later
Solomyak proved that for almost all $\lambda \in (1/2, 1)$ the measure
$\mu_\lambda$ is absolutely continuous, with density in $L^2$. It has
been
conjectured that $\mu_\lambda$ is absolutely continuous for every $\lambda$
in
the interval $(1/2, 1)$ whose reciprocals are not Pisot numbers. In this
talk we
consider the regularity of the density functions of $\mu_\lambda$. We
show that
there are $\lambda$'s such that $\lambda^{-1}$ are not Pisot but the density
functions are not in $L^2$, among other results.