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\section{Development of Methods and Associated Technical Issues}

\subsection{Issues concerning the inclusion of correlations beyond LDA}

\subsubsection{Choice of basis sets for correlated materials}

Discuss the available possibilities (LMTO, PAW, etc...),
and their relative advantages for implementation
of DMFT, or of GW.

\subsubsection{Double counting corrections}

In LDA+U or LDA+DMFT schemes, discuss the various choices for the
double counting correction term. Discuss the influence of this choice on
physical properties like e.g the position of the f-level. Also, issues
of consistency with Luttinger theorem.

\subsubsection{The interaction parameters: U's}

Physical significance of local U's. Relevance of atomic values.
Possibility of ab-initio evaluation.

\subsubsection{GW methods}

Current status of ab-initio calculations of polarisation operators.
The issue of ``self-consistent'' vs. ``non self-consistent'' GW.
Can one combine GW and LDA+DMFT ? For which materials would this be
useful ?
Optical properties of materials.
\subsection{Issues related to the practical implementation of DMFT}

\subsubsection{Impurity solvers}

Accurate and efficient solutions of multi-orbital impurity problems
is key to the success of LDA+DMFT methods (or cluster-DMFT). There are many
issues to discuss there, e.g:

\begin{itemize}

\item How to improve the numerical efficiency of QMC solvers ?

\item NCA: virtues and drawbacks
Recent improvements of NCA.
\item Approximate efficient solvers: low-energy slave bosons, high-energy
equations of motion, etc...

\item Constraints and cross-checks on impurity solvers: sum rules, weight of
Hubbard bands in the multi-orbital case, etc...

\item New algorithms ?

\end{itemize}

There are many other technical points to be discussed: k-sums, analytic
continuation of QMC data, etc...

\subsection{Issues related to cluster (and other)  extensions of DMFT}

\subsubsection{Various cluster schemes}

Discuss the various cluster schemes available. Convergence to thermodynamic
limit, issues of boundary conditions, etc...

\subsubsection{Physics issues related to clusters}

What is our current physical insights into some of the new physics
brought in by cluster schemes: pseudo-gap (short-range AG correlations),
d-wave superconductivity, etc... Connection with known physics of
multi-impurity models. For which materials are cluster schemes essential:
cuprates, 2D organics, etc...

\subsubsection{Pushing the frontier of DMFT}

Extensions of the DMFT scheme to: longer-range interactions (e.g Coulomb, issues
of screening and extended DMFT), extended DMFT cluster schemes for frustrated magnets, etc...

\subsection{Numerical Renormalisation Group Techniques}


\subsubsection{Current status of DMRG}

Where do we stand on: calculation of dynamical response functions, extensions
to higher-dimensional systems, etc...
DMRG for cluster DMFT studies.

\subsubsection{Issues on RG for anisotropic Fermi surfaces}

Significance of strong coupling flows. What have we learned on 2D Hubbard ?
Comparaison of real space and momentum space RG's.

\section{Physical Issues Associated With Specific (Correlated) Materials}

\subsection{Metals close to the Mott transition: 1-particle spectroscopy}

DMFT has provided a quantitative description of the one-particle spectral function
of metals close to the Mott transition. Distinctive aspects are: quasiparticle features
at low energy with reduced weight, Hubbard bands at high energy. There is a separation
of energy scales between these two features. Significant spectral weight transfers
are predicted as temperature is changed.

An important and timely issue to be discussed is: what are the spectroscopic experimental
evidence for this picture ? We could discuss: photoemission, tunnel (STM) measurements, optics.
In materials like: transition metal oxides, 2D organics.

\subsection{Orbital physics in $V_2O_3$}

This is probably one of the oldest and most widely studied correlated electron system.
It displays both Mott transitions and magnetic ordering
transitions. However the nature of the orbital
degrees of freedom continues to be a subject of great debate. Over the last year, some advances in
modelling the orbital ordering in the paramagnetic insulating phase have been made.
Progress has also been achieved within DMFT, on the conceptual understanding
of the critical endpoint of the Mott transition line.
Clearly the time is ripe for a synthesis, including both the charge and orbital dynamics.

\subsection{Manganites}
Origin of giant magnetic resistance, phase diagram.
Interplay of band structure and correlations. 
Electron phonon interactions in correlated materials.

\subsection{Volume-collapse in rare earth and actinides}

Under pressure or as T is varied (Pu, Ce).
Assessment of the limitations of LDA. Magnitude of the volume difference
through the transition region. LDA+DMFT recent results. Degree of correlation
in the ``itinerant'' f-electron side of the transition. Relevance of qualitative
descriptions and mechanisms: Kondo volume collapse vs. Mott. Is this a real debate ?

\subsection{Extreme rare-earths: Cerium and Ytterbium}

Specific difficulties encountered in LDA treatments of these two elements
and their compounds. Possible remedies.

\subsection{Superconductivity of Americium: mechanism.}

\subsection{Issues in transition metal magnetism}

Predicting $T_c$, Fermi surfaces, magnetic anisotropy. Qualitative role of
Hund coupling and lattice geometry. Local moments and ``magnons'' above $T_c$.

Optical conductivity data: can DMFT account more quantitatively for
the anomalous power laws observed ?
To which extent short range order is important in these compounds ?

\subsection{2D Organics}

A case for DMFT at hi-T ? Can it consistently describe transport, thermodynamics
and optics ? Need for AF correlations at lower T. Mechanism of
superconductivity. A case for clusters ?

\subsection{1D organics}

Current understanding and puzzles in 1D organics. DMFT description of the
dimensional crossover.
\subsection{High Temperature superconductors}
What does Tc depend on. Can we raise it.

More generally, different methods for computing critical temperatures
(ferromagnetic, ferroelectric, superconducting)
and how to use them to optimize properties of materials. 



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