Monday 1 August
09:0009:10 • Welcome
09:1010:10 •
Christian Hainzl •
From BCS to GinzburgLandau via a Semiclassical Limit

We give the first rigorous derivation of the GinzburgLandau (GL) theory,
starting from the microscopic BardeenCooperSchrieffer (BCS) model. Close
to the critical temperature, GL arises as an effective theory on the macroscopic
scale. The relevant scaling limit is semiclassical in nature. Additionally, we consider the low
density limit at zero temperature and show that if the interaction potential allows for a
twoparticle bound state, the system is well approximated by the GrossPitaevskii (GP) functional,
describing a BoseEinstein condensate of fermion pairs.

10:1010:30 • Coffee break
10:3011:30 •
Israel Michael Sigal •
Dynamics of Magnetic Vortices

In this talk I will review recent results on existence, stability and dynamics
of solutions of the GinzburgLandau equations of superconductivity exhibiting
the vortex structure.

11:4512:45 •
David Hasler •
Anderson Localization for Random Magnetic Schrödinger Operators

I will consider a twodimensional magnetic Schrödinger operator with a spatially random magnetic field in R^{2} as well as in Z^{2}.
We prove a Wegner estimate which can be used to prove localization at the edges of the spectrum.

12:4515:00 • Lunch
15:0018:00 •
Christian Hainzl, informal lecture on BCS theory
Tuesday 2 August
09:0010:00 •
Markus Holzmann •
Equation of State of Dilute Degenerate Bose Gases

I will discuss the effects of interatomic interactions on the equation of state
of dilute Bosons in two and three dimensions. In particular, I will focus on the
stucture expected close to the superfluid transition (BoseEinstein condensation
in three dimensions or KosterlitzThouless transition in two dimensions) and
consequences for current experiments on trapped atomic gases.

10:0010:30 • Coffee break
10:3011:30 •
Herbert Spohn •
The Retarded van der Waals Potential  A Challenge to Nonrelativistivc QED

We discuss the ground state energy, E(R), of two hydrogen atoms
separated by a distance R and coupled to the Maxwell field, in particular the
CasimirPolder prediction of  R^{7} at large R. This is ongoing joint work with
Tadahiro Miyao.

11:4512:45 •
Stefan Teufel •
Spontaneous Decay of Resonant Energy Levels for Molecules with Moving Nuclei

The goal of this work is to understand spontaneous emission of photons by dynamical
molecules, e.g. during a chemical reaction, in the limit of small coupling to the
field and heavy nuclei. There are two well understood limiting regimes: without
coupling to the field the limit of heavy nuclei yields the BornOppenheimer approximation.
For infinitely heavy nuclei the resonant states of the system have been studied in
great detail during the recent years. We study the combined limit where the lifetime
of the resonances is large on the timescale of nuclear dynamics. In the PauliFierz
model we prove the validity of the BornOppenheimer approximation at leading order
and compute the rate of spontaneous emission of photons.

12:4515:00 • Lunch
15:0018:00 •
Markus Holzmann, informal lecture on the critical temperature of interacting Bose gas
Wednesday 3 August
09:0010:00 •
Alessandro Pizzo •
Absence of Embedded Mass Shells: Cerenkov Radiation and Quantum Friction

We show that, in a model where a nonrelativistic particle is coupled to a quantized
relativistic scalar Bose field, the embedded mass shell of the particle dissolves in
the continuum when the interaction is turned on, provided the coupling constant is
sufficiently small. More precisely, under the assumption that the fiber eigenvectors
corresponding to the putative mass shell are differentiable as functions of the
total momentum of the system, we show that a mass shell could exist only at a strictly
positive distance from the unperturbed embedded mass shell near the boundary of the
energymomentum spectrum. (Joint work with W. De Roeck and J. Fröhlich.)

10:0010:30 • Coffee break
10:3011:30 •
Jürg Fröhlich •
On the Theory of Slowing Down Gracefully

Having just passed from active duty to retirement, the speaker is interested in
manifestations of Aristotle's Law of Motion: "A moving body (e.g. a retired professor)
will come to rest as soon as the force pushing it (his students and postdocs) no
longer acts on it in the manner necessary for its propulsion." The speaker will
consider systems somewhat simpler than a retired professor and formulate Hamiltonian
models of Friction and Diffusion useful to describe them. The Einstein relation between
the speed of a particle in forced motion and the diffusion constant is discussed, too.

11:4512:45 •
Sabine Jansen •
Fermionic and Bosonic Laughlin State on Thick Cylinders

We investigate a manybody wave function for particles on a cylinder known as Laughlin's
function. It is the power of a Vandermonde determinant times a Gaussian. Our main result
is: in a manyparticle limit, at fixed radius, all correlation functions have a unique
limit, and the limit state has a nontrivial period in the axial direction. The result
holds regardless how large the radius is, for fermions as well as bosons. In addition,
we explain how the algebraic structure used in proofs relates to a ground state perturbation
series and to quasistate decompositions, and we show that the monomerdimer function
introduced in an earlier work is an exact, zero energy, ground state of a suitable finite
range Hamiltonian.

12:4515:00 • Lunch
15:0018:00 •
Jürg Fröhlich & Alessandro Pizzo, informal lecture on quantum friction
Thursday 4 August
09:0010:00 •
Antti Knowles •
Spectral and Eigenvector Statistics of Random Matrices

I review recent results on the spectral and eigenvector statistics of large random
matrices. In particular, I cover the bulk and edge universalities of generalized
Wigner matrices. I also outline the universality of eigenvectors associated with
eigenvalues near the spectral edge. In addition to generalized Wigner matrices, I
consider the ErdösRényi graph, and discuss its spectral universality
as well as the complete delocalization of its eigenvectors. Finally, I sketch the
main ingredients of the proofs. (Joint work with L. Erdös, H.T. Yau and J. Yin.)

10:0010:30 • Coffee break
10:3011:30 •
Dirk Hundertmark •
Some Rigorous Results for Dispersion Management Solitons

We describe recent rigorous work on solitonlike pulses in
dispersion managed optical glassfiber cables.
Here ``dispersion management'' refers to the engineering of an optical
fiber channel with alternating spans of positive (normal) and negative
(anomalous) dispersion fiber (periodic or otherwise) in order to
achieve greater stability, bandwidth, etc., of optical information
transfer. This technology has lead to a 100fold increase in bandwidth
in longhaul optical transmission lines over intercontinental distances
and it is widely used commercially nowadays.
The simplest mathematical model describing pulses in a glassfiber cable
is the scalar onedimensional nonlinear Schr\"odinger equation with
cubic nonlinearity. ``Dispersion management'' means that the coefficient
of dispersion is a function of distance (e.g. periodic) along the
fiber waveguide. To model dispersion managed fiber channels one also
averages over one period, yielding the GabitovTuritsyn equation, which
is a nonlocal version of the nonlinear Schr\"odinger equation.
In physical experiments, as well as numerical studies, it has long
been observed that one gets solitonlike localized solutions even
for zero average dispersion! This was a surprise, both physically and
mathematically, because the conventional wisdom had been that solitons
emerge from a combination of nontrivial linear dispersion and nonlinearity.
So something more subtle is going on in the zero average dispersion case,
which is also the most important case from an applications point of view.
Rigorous results on solitonlike pulses for the GabtovTuritsyn
equation, the socalled dispersion management solitons, have been rare
(I know of 6), which is mainly due to its nonlocality, which makes it
hard to study. Rigorous results for zero average dispersion are even
rarer, since this case is a singular limit. This is quite in contrast
to the enormous amount of experimental, numerical and theoretical work
(if one searches for ``dispersion management'' on Google one gets more
than 12 million hits and on Google scholar still roughly 791.000 hits).
We will discuss recent work on the decay and regularity
properties of dispersion management solitons. Our results include a
simple proof of existence of solutions of the dispersion management
equation under mild conditions on the dispersion profile, which includes
all physically relevant cases, regularity of weak solutions, and most
recently a proof of exponential decay of dispersion management solitons,
which confirms the theoretically and experimentally seen fact that dispersion
management solitons are very welllocalized.
This is joint work with YoungRan Lee and Burak Erdo\~{g}an.

11:4512:45 •
Wojciech de Roeck •
TimeDependent Approach to Open Quantum Systems

I present an overview of some recent results on open quantum systems, including
proofs of equilibration, diffusion, and timeindependent photon bounds. The common
strategy is to view the evolution of those open quantum systems as a small deviation
from Markovian behaviour, which can often be established in some scaling limit.
The deviation of the true evolution from the Markovian behaviour is then controlled
with the help of hightemperature expansions, with the coupling playing the role
of inverse temperature. This overview concerns joint works with J.Fröhlich,
A.Pizzo, K.Schnelli and A.Kupiainen.

12:4515:00 • Lunch
15:0018:00 •
Wojciech de Roeck & Antti Knowles, informal lecture on quantum Brownian motion
Friday 5 August
09:0012:30 • Herbert Spohn, informal lecture on the onedimensional KardarParisiZhang equation
15:0018:00 • possible extra informal lecture