




Plenary Speakers / Conférenciers principaux
 JAMES ARTHUR, Toronto
An introduction to the trace formula

The trace formula is a vast generalization of the Poisson summation
formula. It relates rational conjugacy classes on the one hand, with
automorphic representations on the other. The talk will be a general
introduction to the trace formula. We shall also try to give some
indication of how it can be used to study fundamental arithmetic properties
of automorphic representations in terms of corresponding properties of
conjugacy classes.
 FRANCIS CLARKE, Institut Desargues, Université Lyon I, 69622 Villeurbanne,
France
The feedback problem in control theory

In this nontechnical survey, we begin by defining the principal issue
in control theory: to design a feedback law having a certain desired
effect on the underlying dynamical system. The possible contexts in
which this problem can be given a precise formulation are multiple,
depending notably on the type of dynamical system considered, the
degree of knowledge of the model that is assumed, and the goal that is
desired. The actual and potential applications are also widespread,
and very important, encompassing as they do such special cases as
linear systems theory and optimal control. Here we shall focus
primarily upon the stabilization issue for nonlinear systems of
ordinary differential equations, a very active area in the last
decade. Besides discussing some earlier important results, we shall
present more recent work bearing upon the interest (in fact, the
absolute necessity) of using discontinuous feedback laws. In
particular, this work settles an old problem in the field by proving
that every (openloop) controllable system admits a stabilizing
feedback.
 IOANNIS KARATZAS, Columbia
Financial mathematics

 DUSA MCDUFF, Department of Mathematics, SUNY, Stony Brook, New York 11794,
USA
Some open problems in symplectic topology

A symplectic structure is a weakened form of a Kahler structure. Much
of the rigidity of complex geometry is lost in the symplectic world,
but intriguing topological features remain. A good deal is now known
about them, but there are still plenty of open problems. This talk
will discuss some of them, concentrating on questions concerning
diffeomorphisms that preserve the symplectic structure and the groups
that they form.
 EUGENE MYERS, Celera Genomics, Rockville, Maryland 20850, USA
Whole genome assembly of the Drosophila and human genomes

We report on the design of a whole genome shotgun assembler and its
application to the sequencing of the Drosophila and Human genomes.
Celera's whole genome strategy consists of randomly sampling pairs of
sequence reads of length 500600 that are at approximately known
distances from each othershort pairs at a distance of 2K, long pairs
at 10K, and BACend pairs at 150K. For Drosophila, we collected 1.6
million pairs whereby the sum of the lengths of the reads is roughly 13
times the length of the genome ( ~ 120 million), a so called 13X shotgun
data set. The reads were further collected so there are two short read
pairs to every long read pair, with a sprinkling of roughly 12,000
BACend pairs. The experimental accuracy of the read sequences is
roughly 98%. Given this data set, the problem is to determine the
sequence of Drosophila's 4 chromosomes that are estimated to be
510% repetitive sequence.
By layering the ideas of uncontested interval graph collapsing,
confirmed read pairs, and mutually confirming paths, we arrive at a
strategy that makes remarkably few errors. The assembler correctly
identifies all unique stretches of the genome, correctly building
contigs for each and ordering them into scaffolds spanning each of the
chromosomes. We will present our final results for the Drosophila
assembly and report on our progress towards the sequencing and assembly
of the human genome.
 RAYMOND PIERREHUMBERT, Department of Geophysical Sciences, University of Chicago,
Chicago, Illinois, USA
Statistical mechanics of chaotic advectiondiffusion in the atmosphere

``Chaotic AdvectionDiffusion'' refers to the class of
advectiondiffusion problems for which the trajectories induced by the
advecting velocity field are chaotic, i.e. have a positive
Lyapunov exponent. The theory of chaotic advection diffusion has
developed extensively in the past two decades, and for suitably
idealized classes of flows many quantitative predictions can be made.
The main entities treated by the theory are the probability
distributions of concentration fluctuation, of concentration gradient,
and of concentration differences over finite displacements. All these
quantities are of central interest in atmospheric chemistry, in
atmospheric dynamics (when applied to potential vorticity), and in
diagnosis of atmospheric observations.
In this talk, I will survey the theoretical developments, mostly as
applied to oncedifferentiable velocity fields, and discuss attempts to
push the theory to the point to which it can be applied to realistic
large scale atmospheric velocity fields. The ideas arising from simple
models carry over remarkably well, but there is a clear need to better
understand the effects of transport barriers. I will also discuss new
results on the extension to chemically reactive tracers, a subject that
plays a role in chemical combustion and supernova ignition, aside from
its applications to atmospheric chemistry.
 CARL POMERANCE, Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey 07974,
USA
Prime numbers: what we still don't know

The study of prime numbers goes back over two millennia, yet there are
still extremely basic problems that no one can solve. While some of
these problems are exciting just for the intellectual challenge, others
are given urgency by their connection to the security of many modern
forms of cryptography, including those used to protect commerce on the
Internet. In this talk I will highlight a personal top ten of unsolved
problems, and discuss what meager progress we have made.
 MAURICE QUEYRANNE, Faculty of Commerce and Business Administration,
University of British Columbia, Vancouver, British Columbia V6T 1Z2
Scheduling polyhedra: from cutting planes to approximation algorithms

Scheduling problems concern the allocation of resources, usually called
``machines'' or ``processors'', to tasks over time. They arise in
numerous practical applications, in particular in the manufacturing,
computing and communication industries. We will discuss an approach
whereby scheduling problems are modelled as linear programming problems
with a small number of variables (typically, one per job or operation)
and numerous linear constraints that represent or approximate the
scheduling restrictions. This approach relies on the study of
polyhedra that arise as the convex hull of vectors representing
feasible schedules, and was initiated by Balas (1985) and Wolsey
(1985). Some of the main results include the identification of
supermodular polyhedra associated with certain classes of ``easy''
scheduling problems and, for harder problems, of classes of linear
inequalities (cutting planes) that admit efficient separation
algorithms. We will present some recent results with exact solution
methods of the branch and cut type, and approximate algorithms with
bounded performance guarantees, for certain single and parallel machine
shop scheduling problems with precedence constraints and/or release
dates.
 LAWRENCE SHAMPINE, Mathematics Department, Southern Methodist University, Dallas,
Texas 75275, USA
Solving ODEs in new computing environments

For several decades the speaker investigated the numerical
solution of ODEs and developed solvers for general scientific
computation (GSC). In the last several years he has worked on
solving ODEs in a variety of new computing environments that
emphasize convenience. What is there to work on? Why don't you
just translate one of the solvers popular in GSC? You can, and
people have, but this does not provide a quality product because
both the goals and the environments differ in important ways. Case
studies are used to illustrate some of the differences and their
implications for solving ODEs: ODE Architect illustrates packages
for teaching ODEs. The simulation language SIMULINK
illustrates packages for specific applications. Two problem
solving environments are included: MATLAB, which
emphasizes numerical computation, and Maple, which emphasizes
algebraic computation.
 DEMETRI TERZOPOULOS, Toronto

 LOU VAN DEN DRIES, Urbana, Illinois, USA
Logarithmicexponential series

The field of ordinary power series with real coefficients can be
extended to a much larger field of formal series in which operations
such as exponentiation, taking logarithms, derivatives,
antiderivatives, composition and compositional inverse can be carried
out without the usual restrictions. This field of
``logarithmicexponential series'' is a natural domain for the kind of
asymptotic expansions that occur in Hilbert's 16th problem on limit
cycles (work of Ecalle, Il'yashenko). This field of LEseries has also
remarkable algebraic and modeltheoretic properties, such as
ominimality.
 SHINGTUNG YAU, Harvard, USA
PDEto be confirmed

 EFIM I. ZELMANOV, Yale, USA
On some algebraic structures related to conformal field theory

During the last 20 years vertex and conformal algebras found amazing
applications in various areas of physics and mathematics.
We will discuss examples amd classification of algebras of small
GelfandKirillov dimension.

