Monday 1 August

09:00-09:10  •  Welcome

09:10-10:10  •  Christian Hainzl  •  From BCS to Ginzburg-Landau via a Semiclassical Limit
We give the first rigorous derivation of the Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (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 two-particle bound state, the system is well approximated by the Gross-Pitaevskii (GP) functional, describing a Bose-Einstein condensate of fermion pairs.

10:10-10:30  •  Coffee break

10:30-11:30  •  Israel Michael Sigal  •  Dynamics of Magnetic Vortices
In this talk I will review recent results on existence, stability and dynamics of solutions of the Ginzburg-Landau equations of superconductivity exhibiting the vortex structure.

11:45-12:45  •  David Hasler  •  Anderson Localization for Random Magnetic Schrödinger Operators
I will consider a two-dimensional magnetic Schrödinger operator with a spatially random magnetic field in R2 as well as in Z2. We prove a Wegner estimate which can be used to prove localization at the edges of the spectrum.

12:45-15:00  •  Lunch

15:00-18:00  •  Christian Hainzl, informal lecture on BCS theory

Tuesday 2 August

09:00-10:00  •  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 (Bose-Einstein condensation in three dimensions or Kosterlitz-Thouless transition in two dimensions) and consequences for current experiments on trapped atomic gases.

10:00-10:30  •  Coffee break

10:30-11:30  •  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 Casimir-Polder prediction of - R-7 at large R. This is ongoing joint work with Tadahiro Miyao.

11:45-12:45  •  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 Born-Oppenheimer 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 time-scale of nuclear dynamics. In the Pauli-Fierz model we prove the validity of the Born-Oppenheimer approximation at leading order and compute the rate of spontaneous emission of photons.

12:45-15:00  •  Lunch

15:00-18:00  •  Markus Holzmann, informal lecture on the critical temperature of interacting Bose gas

Wednesday 3 August

09:00-10:00  •  Alessandro Pizzo  •  Absence of Embedded Mass Shells: Cerenkov Radiation and Quantum Friction
We show that, in a model where a non-relativistic 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 energy-momentum spectrum. (Joint work with W. De Roeck and J. Fröhlich.)

10:00-10:30  •  Coffee break

10:30-11:30  •  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.

11:45-12:45  •  Sabine Jansen  •  Fermionic and Bosonic Laughlin State on Thick Cylinders
We investigate a many-body 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 many-particle limit, at fixed radius, all correlation functions have a unique limit, and the limit state has a non-trivial 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 quasi-state decompositions, and we show that the monomer-dimer function introduced in an earlier work is an exact, zero energy, ground state of a suitable finite range Hamiltonian.

12:45-15:00  •  Lunch

15:00-18:00  •  Jürg Fröhlich & Alessandro Pizzo, informal lecture on quantum friction

Thursday 4 August

09:00-10:00  •  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 Erdös-Rényi 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.)

10:00-10:30  •  Coffee break

10:30-11:30  •  Dirk Hundertmark  •  Some Rigorous Results for Dispersion Management Solitons
We describe recent rigorous work on soliton-like pulses in dispersion managed optical glass-fiber 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 long-haul optical transmission lines over intercontinental distances and it is widely used commercially nowadays. The simplest mathematical model describing pulses in a glass-fiber cable is the scalar one-dimensional 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 Gabitov-Turitsyn equation, which is a non-local version of the non-linear Schr\"odinger equation. In physical experiments, as well as numerical studies, it has long been observed that one gets soliton-like 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 soliton-like pulses for the Gabtov-Turitsyn equation, the so-called dispersion management solitons, have been rare (I know of 6), which is mainly due to its non-locality, 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 well-localized. This is joint work with Young-Ran Lee and Burak Erdo\~{g}an.

11:45-12:45  •  Wojciech de Roeck  •  Time-Dependent Approach to Open Quantum Systems
I present an overview of some recent results on open quantum systems, including proofs of equilibration, diffusion, and time-independent 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 high-temperature 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.

12:45-15:00  •  Lunch

15:00-18:00  •  Wojciech de Roeck & Antti Knowles, informal lecture on quantum Brownian motion

Friday 5 August

09:00-12:30  •  Herbert Spohn, informal lecture on the one-dimensional Kardar-Parisi-Zhang equation

15:00-18:00  •  possible extra informal lecture