For suggestions, questions etc. please contact Galia Dafni (gdafni@mathstat.concordia.ca), Dmitry Jakobson (jakobson@math.mcgill.ca) or Alexander Shnirelman (shnirel@mathstat.concordia.ca)

** Wednesday, September 8, Time and Room TBA**

**Elijah Liflyand** (Bar Ilan)

Title TBA

** Please note, that friday seminars at McGill in winter 2010
will often be held from 13:30-14:30 (1 hour earlier!) in Burnside 920
(same room as before). **

Height dependent mean curvature equation

Partial regularity for some regularized Navier-Stokes equations

The scaling limit of the critical one-dimensional random Schrodinger operator

(H

ψ

in the scaling limit Var(v

A sharp rearrangement inequality for the Coulomb energy

I will discuss this question in the context of recent results (due to Fusco, Maggi, Pratelli and others) that bound the "asymmetry" of a body in terms of its "isoperimetric deficit". Much less is known about inequalities for multiple integrals; in some cases, not even all optimizers have been identified. I will present a recent result on the Coulomb energy, sketch its proof, and mention open problems.

On the idea of ensemble

Non-random perturbation of Anderson hamiltonian

Solving Dirichlet problem, barriers with logarithmic growth, and boundary geometry

The critical temperature of dilute Bose gases

The Mass critical fourth order Schrodinger equation

Isoperimetric and Concentration Inequalities, and their applications

2D Schrodinger with a strong magnetic field: dynamics and spectral asymptotics near boundary

$$ H=\bigl(h\nabla - \mu \mathbf{A}(x)\bigr)^2 +V(x), \qquad \mathbf{A}(x)=(-\frac{1}{2}x_2, \frac{1}{2}x_1)$$

(or more general one) and derive rather sharp asymptotics of $ \int \psi (x)\, e(x,x,0)\,dx$ as $\mu\to\infty$ and $h\to 0$ where $e(x,y,\lambda)$ is a Schwartz kernel of spectral projector of $H$ and $\psi(x)$ is a cut-off function. Corresponding classical dynamics associaated with operator in question inside of domain is a cyclotron movement along circles of radius $\asymp \mu^{-1}$ combined with slow drift movement (with a speed $\asymp \mu^{-1}$) along level lines of $V(x)$. However near boundary dynamics consists of hops along it; this hop dynamics could be torn away from the boundary and become an inner dynamics and v.v. This classical dynamics has profound implications for spectral asymptotics (with remainder estimate better than $O(h^{-1})$ and up to $O( \mu^{-1}h^{-1})$). We consider also the case of superstrong magnetic field (as $\mu h\ge 1$) when classical dynamics is at least applicable but the difference between Dirichlet and Neumann boundary conditions are the most drastic.

The full and detailed analysis: Chapter 15 of My Future Monster Book

What is the boundary value of a holomorphic function?

Semiclassical Limits of eigenfunctions on flat n-dimensional tori

Quasiconformal mappings, isoperimetric inequality and finite total Q-curvature

Parabolic BMO and A_p classes

Do minimizers of causal variational principles have a discrete structure?

From Spectral Theory of Polyhedral Surfaces to Geometry of Hurwitz Spaces

Optimal multidimensional pricing facing informational asymmetry

Newton-conjugate-gradient methods for solitary wave computations

Surface Evolution under Curvature Flows - Existence and Optimal Regularity

** Friday, July 17, 14:30-15:30, Burnside 920**

**Jerome Vetois** (Cergy Pontoise)

Bubble tree decompositions for critical anisotropic equations

** Abstract:** We describe the asymptotic behavior in energy space of
Palais-Smale sequences for an anisotropic problem on a domain in the
Euclidian space. This description is well-known in the isotropic case.
In the general case, we emphasize the crucial role played by the
geometry of the domain.

On radial and conical Fourier multipliers

On threshold eigenvalues and resonances for the linearized NLS equation

Breakdown of Analyticity: Rigorous results and numerical implementations

Critical points and level sets of solutions to elliptic PDEs

\Delta u=0\quad {\rm in }\;\mathbf{R}^n\backslash\overline{\Omega},\quad u|_{\partial\Omega}=1,

with $u\to 0$ at infinity and $\Omega$ being a bounded domain with $C^{2,\alpha}$ connected boundary. We shall prove that the critical set of $u$ can be nonempty (in fact, of codimension $3$) even when $\Omega$ is contractible, thereby settling a question posed by Kawohl in 1988, discuss sufficient geometric criteria for the absence of critical points in this problem and analyze the properties of the critical set for generic domains. Time permitting, related problems on Riemannian manifolds will be discussed as well. Our results hinge on a combination of classical potential theory, transversality techniques and the qualitative theory of dynamical systems.

Asymptotic expansion of the integrated density of states of a two-dimensional periodic Schrodinger operator

Valuations on Convex Sets and Sobolev Functions

Central limit theorem for sums of non-commutative i.i.d random variables

Invariant and stationary measures for groups of toral automorphisms

Curvature of Random Metrics

Eigenfunction concentration and non-concentration

Strong A-infinity weights and Sobolev capacities in metric measure spaces

On the adiabatic perturbation theory and the piston problem

Rapid Evolution of Complex Limit Cycles

Billiard Models and Energy Transfer

UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420

Structure of attractors for (a,b)-continued fraction transformations

Rapid evolution of complex limit cycles

CRM, Salle 5340, Pav. Andre Aisenstadt, 2920 Chemin de la Tour, Universite de Montreal.

On generalizations of Littlewood-paley inequalities to domains in R

Concordia University, Library building, 9th floor, room LB 921-4

The Existence of the Lorenz strange attractor

UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420

Kakeya-Nikodym averages and Lp norms of eigenfunctions

Meeting Room: CRM, Pav. Andre-Aisenstadt, Room 6214

Details: see conference page and schedule

2005/2006 Analysis Seminar

2004/2005 Seminar in Nonlinear Analysis and Dynamical Systems

2003/2004 Working Seminar in Mathematical Physics