For suggestions, questions etc. please contact Dmitry Jakobson (jakobson@math.mcgill.ca), Alina Stancu (stancu@mathstat.concordia.ca), or Alexey Kokotov (alexey@mathstat.concordia.ca)

** Friday, June 21, 13:30-14:30, Burnside 920**

** Guofang Wang** (Freiburg)

Mass and geometric inequalities

**Absract:** In this talk, we start from a new mass for
asymptotically flat manifolds and prove a positive mass
theorem and a Penrose type inequality for asymptotically
flat graphs, by using classical Alexandrov-Fenchel
inequalities in the euclidean space. Then we define a new
mass for asymptotically hyperbolic manifolds and prove
a positive mass theorem and a Penrose type inequality
for asymptotically hyperbolic graphs, by establishing
new weighted Alexendrov-Fenchel inequalities in hyperbolic space

**Monday, January 14, 13:30-14:30,
Burnside 920**

**Phan Thanh Nam** (Universite de Cergy-Pontoise)

Bogoliubov spectrum of interacting Bose gases

** Abstract:**In 1947 Bogoliubov predicted that the excitation
spectrum of some certain N-body Bose gas can be approximated by that
of the so-called Bogoliubov Hamiltonian in Fock space. This prediction
was proved recently for systems with short range potentials by Seiringer
(2011) and Grech-Seiringer (2012). In this talk, we shall give abstract
conditions on which Bogoliubov's theory is valid. Then we apply the method
to some Coulomb systems. This is joint work with Mathieu Lewin, Sylvia
Serfaty and Jan Philip Solovej.

Geodesics in the space of Kahler metrics

Tire tracks geometry, hatchet planimeter, Menzin's conjecture, and complete integrability

Gaussian free field, random measure and KPZ on R^4.

Hadamard states: from solutions of the Klein-Gordon equation to renormalised quantum fields

A Probabilist's Thoughts about a Theorem of L. Hormander

Perturbative Approach to AQFT and KMS states

A correspondence between conformal field theory and Teichmuller theory

Applications of repeated interaction systems

1. return to equilibrium in a QED cavity (one-atom maser experiment)

2. a toy model describing the establishment of a dc current in a tight-binding band.

Constructing explicitly parametrized minimal tori in spheres via Takahashi's theorem

Operators and Perturbations

List of subjects that will be (partially) covered:

1) Reminder of basic spectral theory

- Unbounded operators

- Closed operators

- Spectrum

- Pseudoresolvents

- Unbounded operators on Hilbert spaces

- (Essential) self-adjointness

- Relative boundedness

- Scale of Hilbert spaces

- Closed and closable positive forms

- Relative form boundedness

- Friedrichs extensions

2) Reminder of basic harmonic analysis and its applications

- Young inequality

- Sobolev inequalities

- Application: self-adjointness of Schrodinger operators

3) Momentum and Laplacian in 1 dimension

- Momentum on half-line

- Momentum on an interval

- Laplacian on half-line

- Laplacian on an interval

4) Orthogonal polynomials

- Orthogonal polynomials in weighted L

- Self-adjointness of Sturm-Liouville operators

- Classical orthogonal polynomials as eigenvectors of certain Sturm-Liouville operators

- Hermite polynomials

- Laguerre polynomials

- Jacobi polynomials

5) Finite rank perturbations and their renormalization

- Aronszajn-Donoghue Hamiltonians

- Delta potentials

- Friedrichs Hamiltonians

- Bound states and resonances of Friedrichs Hamiltonians

- Exponential decay from a unitary dynamics

6) Potential 1/|x|

- Hardy inequality

- Modified Bessel equation

- Bessel equation

- Operator -d

Knotted vortex tubes in steady Euler flows

Hardy inequalities on mean convex domains

The linearized Monge-Ampere equation and its geometric applications

Resonances in Scattering by Two magnetic Fields at Large Separation and a Complex Scaling Method

The supremum of L^2 normalized random holomorphic fields

Weighted Paley-Wiener Spaces and MC-Spaces

Spectral theory of multidimensional periodic and almost-periodic operators: Bethe-Sommerfeld conjecture and the integrated density of states.

1. Bethe-Sommerfeld Conjecture. For a large class of multidimensional periodic operators the numbers of spectral gaps is finite.

2. Asymptotic behaviour of the integrated density of states of periodic and almost-periodic operators for large energies.

Chern-Simons invariants, determinant of Laplacian, and tau functions

Geodesics of Random Riemannian Metrics

Spectral Minimal Partitions

Generic properties of surfaces with cusps

The talk is CANCELLED

Braids and L^p-norms of area-preserving diffeomorphisms

This talk is based on a joint work with Michael Brandenbursky.

The half space property and entire minimal graphs in MxR

Proof of a 35 Year Old Conjecture for the Entropy of SU(2) Coherent States, and its Generalization

Eigenproblems, numerical approximation and proof

Moser averaging

Smoothness properties for some infinite-dimensional heat kernel measures

Quantum correlations and Tsirelson's problem

Dixmier's Similarity Problem

**Friday, September 7, 14:30-15:30,
Burnside 920**

**Nadia Sidorova** (University College, London)

Localisation in the parabolic Anderson model

** Abstract:**
The parabolic Anderson problem is the Cauchy problem for the heat
equation on the d-dimensional integer lattice with random potential.
It describes the mass transport through a random field of sinks and
sources and is actively studied in mathematical physics. We discuss,
for a class of i.i.d. potentials, the intermittency effect occurring
for such potentials, which manifests itself in increasing localisation
and randomisation of the solution.

Nodal sets and negative eigenvalues in conformal geometry

The Jacobi Ensemble and Discrete Uncertainty Principles

The talk is CANCELLED

Evolving Irregular Domains and a Generalized Transport Theorem

Integrability of the Fourier transform: functions of bounded variation

Space of completely bounded L

Abstract

The Willmore functional on the space of complete minimal surfaces in hyperbolic space: Boundary regularity and Bubbles.

Hodge cohomology of iterated fibred cusp metrics on Witt spaces

Inverse scattering at fixed energy in black hole spacetimes.

Two-component Bose-Einstein Condensates

On the analyticity of particle trajectories in the flows of ideal incompressible fluid.

Positive definite decomposition of Green's functions

Geodesics in the space of Kahler potentials

Microlocal analysis of radial points

Invitation a la geometrie aleatoire en dimension superieure a deux

Weighted Paley-Wiener Spaces and MC-Spaces

Graphene operator pencil

Conic Degeneration and the Determinant of the Laplacian.

A glimpse at the differential topology and geometry of optimal transportation

Symmetry and Reflection Positivity

Distribution of random perturbations of propagated eigenfunctions.

Uniform spectral stability for rough perturbations of domains.

(Do) we understand quantum mechanics - finally (?)!

Dissipative motion from a Hamiltonian point of view

Expander Graphs, Thin Groups, and Superstrong Approximation

** Wednesday, June 6, 12:30pm, Burnside 1214**

** Daniel Ueltschi** (University of Warwick)

Introduction to cluster expansions: applications, combinatorics, tree estimates

A priori estimates of prescribing curvature measure problems in Riemann spaces

Composition Operators on Dirichlet series

Sign-changing blow-up for scalar curvature type equations

Similitude pour les operateurs de classe C_0

A Discrete Bernoulli Free Boundary Problem

On minimizers of the bending energy of two-phase biomembranes

2005/2006 Analysis Seminar

2004/2005 Seminar in Nonlinear Analysis and Dynamical Systems

2003/2004 Working Seminar in Mathematical Physics