2008/2009 Analysis Seminar
Seminars are usually held on Mondays or Fridays at Concordia or at McGill
For suggestions, questions etc. please contact Galia Dafni
(gdafni@mathstat.concordia.ca), Dmitry Jakobson
(jakobson@math.mcgill.ca), Ivo Klemes (klemes@math.mcgill.ca)
or Alexander Shnirelman (shnirel@mathstat.concordia.ca)
WINTER 2009
Joint Seminar with Applied Mathematics
Monday, January 12, 2009, 14:30, Burnside 1205
David Anderson (Wisconsin)
Deterministic and Stochastic Methods for Biochemical Reaction Systems
Abastract:
The dynamics of biochemical reaction systems can be modeled either
deterministically or stochastically. Typically, the equations governing
the dynamics of these models are quite complex. Further, there is
oftentimes little knowledge about the exact values of the different
system parameters, and, worse still, these system parameter values may
vary from cell to cell. However, the network structure of a given system
induces the corresponding equations (up to parameter values) governing
its dynamics. I will show in this talk how this fact may be exploited to
infer qualitative properties of large classes of biochemical systems
and, most importantly, to learn which properties are independent of the
details of the system parameters. I will give results for both
stochastically and deterministically modeled systems. I will also
discuss some recent work on numerical methods for the simulation of
sample paths for stochastically modeled systems. The use of such
methods is
quickly increasing throughout the biology and biochemistry
communities and therefore warrants more careful study.
Joint Seminar with Applied Mathematics
Monday, January 19, 2009, 14:30, Burnside 1205
Irina Mitrea (Virginia)
Boundary value problems for higher order elliptic operators
Abstract
Joint Seminar with Applied Mathematics
Monday, January 26, 2009, 14:30, Burnside 1205
Vera Mikyoung Hur (MIT)
Dispersive properties of the surface water waves
Abstract: I will speak on the dispersive character of waves
on the interface between
vacuum and water under the influence of gravity and surface tension. I will
begin by giving a precise account of the formulation of the surface
water-wave problem and discussion of its distinct features. They include the
dispersion relation, its severe nonlinearity, traveling waves and the
Hamiltonian structure. I will describe the recent work of Hans Christianson,
Gigliola Staffilani and myself on the local smoothing effect of 1/4
derivative for the fully nonlinear problem under surface tension with some
detail of the proof. If time permits, I will explore some oen questions
regarding long-time behavior and stability.
Joint Seminar with Applied Mathematics
Monday, February 9, 2009, 14:30, Burnside 1205
George Haller (Morgan Stanley and MIT)
Aerodynamic Separation and Invariant Manifolds: Recent Progress on
a Century-old Problem
Abstract: Flow separation - the detachment of fluid from a
boundary - is a major
cause of performance loss in engineering devices such as diffusers,
airfoils and jet engines. In a landmark 1904 paper on boundary
layers, Ludwig Prandtl derived a criterion for flow separation from
no-slip boundaries in steady two-dimensional incompressible flows.
Despite widespread effort, however, no unsteady or three-dimensional
extension of Prandtl's criterion has emerged in the fluid dynamics
literature.
In this talk, I discuss recent success in extending Prandtl's
criterion to unsteady three-dimensional compressible flows. This new
separation theory relies on nonstandard dynamical systems concepts,
such as nonhyperbolic invariant manifold theory and aperiodic
averaging. Remarkably, these techniques render exact flow separation
criteria that cannot be obtained from first principles. Beyond
discussing the mathematics behind this new theory, I show
numerical and experimental results condirming the new separation
criteria. I also discuss applications to flow control and pollution
tracking.
Joint Seminar with Applied Mathematics
Monday, February 16, 2009, 14:30, Burnside 1205
Rustum Choksi (Simon Fraser)
Mathematical Paradigms for Periodic Phase Separation and Self-Assembly
of Diblock Copolymers
Abstract Energy-driven pattern formation induced by competing
short and long-range interactions is ubiquitous in science, and provides
a source of many challenging problems in nonlinear analysis. One
example is self-assembly of diblock copolymers. Phase separation of the
distinct but bonded chains in dibock copolymers gives rise to an
amazingly rich class of nanostructures which allow for the synthesis
of materials with tailor made mechanical, chemical and electrical
properties. Thus one of the main challenges is to describe and
predict the self-assembled nanostructure given a set of material parameters.
A density functional theory of Ohta and Kawasaki gives rise to nonlocal
perturbations of the well-studied Cahn-Hilliard and isoperimetric
variational problems. In this talk, I will discuss these simple but
rich variational problems in the context of diblock copolymers.
Via a combination of rigorous analysis and numerical simulations in 3D,
I will attempt to characterize minimizers without any preassigned bias
for their geometry. In particular, I will show how this simple model
has given rise to some basic questions and answers in
the modern calculus of variations.
Friday, February 20, 2009, Burnside 920, 14:30
Nadine Badr (CRM and Concordia)
Lp Boundedness of Riesz transform related to Schrodinger
operators on a manifold
Abstract
Friday, March 6, 2009, 14:30, Burnside 920
Ivana Alexandrova (East Carolina)
The Structure of the Scattering Amplitude for Schrodinger
Operators with a Strong Magnetic Field
Abstract: We study the microlocal structure of the
semi-classical scattering amplitude for Schrodinger operators with a
strong magnetic field at non-trapping energies.
We prove that, up to any order, the scattering amplitude can be approximated
by a semi-classical pseudodifferential-operator-valued Fourier integral
operator.
Monday, March 9, 2009, 14:30, Burnside 920
S. Molchanov (North Carolina, Charlotte)
The statistics of the discrete spectrum for the Schrodinger operator with
complex-valued potentials (with applications to optical waveguides).
Joint Seminar with Applied Mathematics
Wednesday, March 11, 2009, 14:30, Burnside 1205
Dmitry Pelinovsky (McMaster)
Global well-posedness and wave breaking in the short-pulse equation
Abastract:
We prove global well-posedness of the short-pulse equation with small
initial data in Sobolev space H^2. Our analysis relies on local
well-posedness results of Schafer & Wayne (2004), the correspondence of the
short-pulse equation to the sine-Gordon equation in characteristic
coordinates, and a number of conserved quantities of the short-pulse
equation. We also find sufficient conditions for the wave breaking to occur
if the initial data have large H^2 norm. The analysis relies on the method
of characteristics and it holds both on an infinite line and in a periodic
domain. Numerical illustrations of the finite-time wave breaking are given
for the periodic short-pulse equation.
Friday, March 13, 2009, 14:30, Burnside 920
Mike Wilson (Vermont)
How fast and in what sense(s) does the Calderon reproducing
formula converge?
Abstract
Monday, March 16, 2009, 14:30, Burnside 920
A. Choffrut (Minnesota)
On steady-state solutions to Euler's equations
Abstract: The manifold of the steady-state solutions of 2d
Euler's equation in a
domain (and with suitable boundary conditions) is typically
infinite-dimensional. The geometric interpretation of Euler's equations
suggests a natural local parametrization of the manifold (under some
non-degeneracy assumptions). This is established rigorously in some
interesting situations. (Joint work with Vladimir Sverak).
Friday, March 20, 14:30, Burnside 920
Raphael Ponge (Toronto)
Pseudodifferential operators and Fefferman's program
Abstract: Motivated by the analysis of the Bergman kernel
of a strictly
pseudoconvex domain of C^n, Fefferman launched in the 70s the
program of determining all the local invariants of a strictly pseudoconvex
CR structure. Since then the program has evolved to include local and global
invariants of other parabolic geometries (e.g. conformal geometry). In this
talk we shall report on approach of Fefferman's program in terms of
pseudodifferential and how this approach allows us to obtain new invariants
in conformal and CR geometry.
Friday, March 27, 14:30, Burnside 920
G. Kolutsky (Moscow, visiting Toronto)
Geometrical Continued Fractions and Anosov Diffeomorphisms
Abstract: We show how an object from the combinatorially geometric
version of the analytical number theory, namely geometrical continued
fractions, appears in the classical smooth dynamics, namely in the
problem on the topological classification of Anosov diffeomorphisms
of tori.
Friday, April 3, 14:30, Burnside 920
Mar Gonzalez (IAS)
Half-Laplacian problems related to crystal dislocations
Abstract: Dislocations are line defects in crystals, and can
be modeled using
non-local operators. I will speak about a related evolution equation
involving the half-Laplacian operator.
Thursday, April 16, 2009, 14:30, Burnside 1205 (please
note day and room change)
Alain Pajor (Marne-la-Valee)
Compress sensing and geometry of polytopes
Abstract: The connection between "Compressed sensing" and
"High dimensional Geometry and Convexity" is well known and studied
in many papers in the recent years. In this talk we will give new
examples of (random) highly neighborly polytopes which in compressed
sensing theory means new examples of "sensing" matrices for the exact
reconstruction of sparse vectors.
Friday, May 1, 2009, 14:30, Burnside 920
R. Martin (UC Berkeley)
Symmetric operators and reproducing kernel Hilbert spaces
Abstract
Tuesday, May 26, 14:30-15:30, Burnside 920
Leonid Berlyand (Penn State)
Homogenization of elasticity equations without scale
separation
Abstract
Wednesday, June 3, 14:30-15:30, Burnside 1214
Paolo Salani (Florence)
Concavity properties and Brunn-Minkowski inequalities in free
boundary problems
Abstract: In a recent paper with C. Bianchini, we prove some concavity
properties connected to nonlinear Bernoulli type free boundary
problems. In particular, we prove a Brunn-Minkowski inequality and an
Urysohn's type inequality for the Bernoulli Constant, giving a partial
answer to a conjecture of Flucher and Rumpf. Moreover, we study the
behaviour of the free boundary with respect to the given boundary data
and we prove a uniqueness result regarding the interior problem.
Friday, June 26, 14:30-15:30, Burnside 920
Junfang Li (Alabama)
Li-Yau type Differential Harnack inequalities on Riemannian
manifolds : linear heat equation
Abstract: We present new Li-Yau type gradient estimates for positive
solutions of heat equation on Riemmannian manifolds with $Ricci(M)\ge -k$,
$k\in \mathbb R$. As applications, several parabolic Harnack inequalities
are obtained and they lead to new estimates on heat kernels of manifolds
with Ricci curvature bounded from below. In the second part, we establish
a Perelman type Li-Yau-Hamilton differential Harnack inequality for heat
kernels on manifolds with $Ricci(M)\ge -k$, which generalizes a result of
L. Ni [NL1,NL4].
As applications, we obtain new Harnack inequalities
and heat kernel estimates on general manifolds. We also obtain various
entropy monotonicity formulas for all compact Riemannian manifolds.
ANALYSIS-REALTED TALKS ELSEWHERE, WINTER 2009
Applied Mathematics: Friday, January 16, 2009, 14:30-15:30,
Burnside 1205
Margaret Beck
Nonlinear stability of time-periodic viscous shocks
Abstract: If a given solution of a PDE is stable, then, roughly
speaking, any other solution that starts near it, stays near it for
all time. This is an important concept in applications, because it is
typically only the stable solutions that are observed in practice. I
will outline two key mathematical difficulties that one can encounter
when analyzing the stability of time-periodic solutions of dissipative
PDEs on unbounded domains. Briefly, they are the presence of zero
eigenvalues that are embedded in the continuous spectrum and the time-
periodicity of the associated linear operator. In the context of
viscous shocks in systems of conservation laws, I will show how these
difficulties can be overcome. The method involves the development of a
contour integral representation of the linear evolution, similar to
that of a strongly continuous semigroup, and detailed pointwise
estimates on the resultant Greens function, which are sufficient for
proving nonlinear stability under the necessary assumption of spectral
stability.
Dynamical Systems seminar: Friday, January 30, 2009, 10:00-11:00
Concordia, Library Building LB 921-4
Edson Vargas (Univ. of Sao Paolo)
Decay of geometry for Fibonacci critical covering maps of the circle
Abstract: We study the growth of Dfn(f(c)) when f is a Fibonacci
critical covering map of the circle with negative Schwarzian
derivative, degree d >= 2 and critical point c of order l > 1. As
an application we prove that f exhibits exponential decay of geometry
if and only if l <= 2, and in this case it has an absolutely
continuous invariant probability measure, although not satisfying
the so-called Collet-Eckmann condition
FALL 2008
Friday, September 5, 2008, 14:30-15:30, Burnside 920
C.S. Lin (National Taiwan University)
Green function, elliptic functions and mead field
equations on torus
Abstract: A mean field equations on torus is a second order nonlinear
ellitpic equations with an exponential nonlinearity. The
blowing up analysis of mean field equation has a close relations
to the critical points of Green function on torus. In this
talk, we will study the question of the number of critical
points of a Green function via the mean field equations.
We prove that the Green function has at most five critical
points via studying the mean curvature equation.
Mini-course by David Ruelle (IHES)
Nonequilibrium statistical mechanics and smooth
dynamical systems
Friday 13:00-14:30, starting September 12; Burnside 920
Description (pdf)
Friday, September 19, 2008, 14:30-15:30, Burnside 920
D. Grieser (Oldenburg)
Spectral approximation for fat graphs
Abstract:
A fat graph is a family of Riemannian manifolds $M_\epsilon$,
$\epsilon>0$, modelled on a finite metric graph $G$, in a way similar to
an $\epsilon$-neighborhood of a straight-edge embedding of $G$ in some
Euclidean space. The behavior of the spectrum and of spectral invariants
of various geometric differential operators on $M_\epsilon$ as
$\epsilon$ tends to zero has been studied by many authors in different
contexts. We focus on a question arising in mathematical physics which
has attracted much attention in the quantum graphs community recently:
Which operator on the singular limit $G$ describes the asymptotic
behavior of the eigenvalues of the Laplacian on $M_\epsilon$
appropriately? While for Neumann boundary conditions (or closed
manifolds) the answer has been known for some time and can be obtained
by relatively elementary methods, the case of Dirichlet conditions is harder
and was solved only recently. This will be explained in the talk.
Joint Seminar with Applied Mathematics
Friday, October 3, 2008, 14:30, Burnside 1205
D. Pelinovsky (McMaster)
Spectrum of an advection-diffusion operator with
sign-varying diffision coefficient
Monday, October 6, 2008, 14:30, Burnside 920
V. Zagrebnov (CPT-Luminy, Marseille)
Bose-Condensation in External Potentials
Abstract (pdf)
Wednesday, October 15, 2008, 13:30-14:30, Room 920
L. Nirenberg (Courant)
Remarks on fully nonlinear elliptic partial differential equations
Friday, October 24, 2008, 14:30-15:30, Burnside 920
S. Janson (Uppsala University)
Schatten norm identities for Hankel operators
Wednesday, October 29 (note a change of date),
13:30-14:30, Room 920
Robert Seiringer (Princeton)
Vortices and Spontaneous Symmetry Breaking in Rotating Bose Gases
Abstract
We present a rigorous proof of the appearance of quantized
vortices
in dilute trapped Bose gases with repulsive two-body interactions
subject to rotation, which was obtained recently in joint work with
Elliott Lieb. Starting from the many-body Schroedinger
equation, we show that the ground state of such gases is, in a
suitable limit, well described by the nonlinear Gross-Pitaevskii
equation. In the case of axially symmetric traps, our results show
that the appearance of quantized vortices causes spontaneous
symmetry breaking in the ground state.
Joint Seminar with Group Theory
Friday, November 7, 2008, 14:30, Burnside 920
A. Furman (Univ. of Illinois at Chicago)
Actions of Product Groups on Manifolds
Abstract This is a joint work with Nicolas Monod. We analyze
volume-preserving
actions of products of Kazhdan groups on Riemannian manifolds.
Under a natural irreducibility assumption we obtain lower bounds on
the dimension of the manifold in terms of the number of factors in
the acting group, and strong restrictions for actions of non-linear
groups. We prove our results by means of a new cocycle superrigidity theorem
of independent interest, in analogy to Zimmer's programme.
Joint Seminar with Vermont
Monday, November 10, 2008, 14:30, Burnside 920
C. Perez (University of Seville)
Weighted estimates Singular Integral Operators and Sobolev inequalities
Abstract (pdf)
Friday, November 21, 2008, 14:30, Burnside 920
A. Komech (Texas A & M)
Global attraction to solitary waves in nonlinear models
based on the Klein-Gordon equation
Abstract: We discuss recent results on global attraction to solitary
waves in several U(1)-invariant models built upon the
Klein-Gordon equation, such as the Klein-Gordon field
interacting with finitely many nonlinear oscillators and
with the mean field interaction.
The main analytical tools of the approach are the Paley-Wiener
arguments and the Titchmarsh Convolution Theorem, which allow
to restrict the time-spectrum of the omega-limit trajectory to
a single point.
Physically, the global attraction to the set of solitary waves
is caused by the nonlinear energy transfer from lower harmonics
to the continuous spectrum and subsequent dispersive radiation.
This is a joint work with Alexander Komech, University of Vienna
Monday, December 1, 2008, 14:30, Burnside 920
W. Craig (McMaster)
The Navier - Stokes equations: an analysis overview
Monday, December 15, 2008, 12:30-13:30, Burnside 920
E. Kritchevski (UBC)
One dimensional Anderson model with non-homogeneous disorder
Abstract: We consider the random discrete Schrodinger operator H=L+V
on the one dimensional integer lattice Z. The operator L is the discrete
laplacian, (LF)(x)=f(x-1)+f(x+1), and V is a potantial, Vf(x)=v(x)f(x),
where v(x) is a family of independent random variables. We will discuss
a new method to establish localization, i.e. that generically the
eigenfunctions of H decay exponentially. The method is robust enough to allow
v(x) to have different probability distributions for different lattice
points x. Moreover, the method allows to obtain lower bounds for the rate
of decay of the eigenfunctions. The talk will be iven in the language of
finite dimensional matrices and basic probability theory.
ANALYSIS-REALTED TALKS ELSEWHERE, FALL 2008
Thursday, September 4, 2008, 13:00; McGill, Rutherford 326
G. Ben-Shach (McGill)
The Isospectral Fruits of Representation Theory: Quantum
Graphs and Drums
CRM-ISM colloquium
Friday, September 26, 4:00-5:00pm
UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420
Vladimir Sverak (University of Minnesota)
PDE aspects of the Navier-Stokes Equations
Abstract: We will explain the main difficulties arising
in the mathematical analysis of the Navier-Stokes equations
and we mention some recent results which are related to these problems.
CRM-ISM colloquium
Friday, October 3, 4:00-5:00pm
UdeM, Pav. Andre-Aisenstadt, 2920, ch. de la Tour, salle 6214
Elliott Lieb (Princeton University)
Some Calculus of Variations Problems in Quantum Mechanics
Abstract:
Three examples are given, in order of historical development, of
minimization problems in quantum mechanics arising from attempts to
model the N-body Schroedinger equation by simpler energy functionals
involving only densities. These simpler models are Thomas-Fermi theory,
Hartree-Fock theory and the Mueller density matrix functional theory.
This talk is for non-specialists: no knowledge of quantum mechanics is needed.
CRM-ISM colloquium
Friday, October 10, 4:00-5:00pm
UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420
Leonid Bunimovich (Georgia tech)
Visual Chaos: dispersing, defocusing, absolute focusing
and astigmatism
Abstract: The mechanisms generating chaotic (hyperbolic)
behavior in billiards will be
discussed. It turned out that all focusing components of the boundary of
chaotic billiards should be absolutely focusing. Absolute focusing seems to
be a new notion in the geometric optics. The astigmatism comes into play in
dimensions greater than two which forces to reduce the sizes of focusing
components of chaotic billiard tables. We conclude with the simple visual
examples of billiards with divided phase space where any number of chaotic
ergodic components coexist with any number of integrable islands.
Andre Aisenstadt lectures
October 17, 20, 22, 23, 4:00-5:00pm
UdeM, Pav. Andre-Aisenstadt, 2920, ch. de la Tour, salle 1360 (Oct. 17);
salle 6214 (Oct. 20, 22, 23)
Svante Janson (Uppsala)
Random Graphs
Abstract
CRM-ISM colloquium
Friday, October 24, 4:00-5:00pm
UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420
David Ruelle (IHES)
Nonequilibrium Statistical Mechanics and Smooth Dynamical Systems
Abstract: One idealization of nonequilibrium statistical
mechanics simply gives general smooth dynamics on a compact manifold,
with new interpretations and new questions, which we shall review.
In particular we shall introduce the natural physical (SRB) measure
associated with a diffeomorphism f, and ask if it depends smoothly
on f. We shall also introduce an analytic susceptibility function
and study its singularities.
CRM-ISM colloquium
Friday, October 31, 4:00-5:00pm
Robert Seiringer (Princeton)
Dilute Quantum Gases
Abstract: We present an overview of mathematical results on the low
temperature properties of dilute quantum gases, which have been obtained in
the past few years. The discussion includes, for instance, results on the
free energy in the thermodynamic limit, and on Bose-Einstein condensation,
Superfluidity and quantized vortices in trapped gases. All these properties
are intensely being studied in current experiments on cold atomic gases. We
will give a brief description of the mathematics involved in understanding
these phenomena, starting from the underlying many-body Schroedinger
equation.
Statistics Journal Club , Burnside 1214
Friday, November 28, 12:00-13:00
Igor Wigman (CRM)
Nodal lines and the distribution of the zeros of random
trigonometric polynomials
Abstract: I will show a video and some pictures of nodal lines,
mysterious lines occuring on musical instruments. I will also explain a
recent related result concerning the distribution of the zeros of random
trigonometric polynomials due to A. Granville-IW.
Workshop at CRM
Hilbert Spaces of Analytic Functions
December 8-12, 2008
Organizers: J. Mashreghi, T. Ransford (Laval),
K. Seip (NTNU)
2007/2008 Seminars
2006/2007 Seminars
2005/2006 Analysis Seminar
2004/2005 Seminars
2004/2005 Seminar in Nonlinear Analysis and Dynamical Systems
2003/2004 Working Seminar in Mathematical Physics
2002/2003 Seminars
2001/2002 Seminars
2000/2001 Seminars
1999/2000 Seminars