In 2009 and 2011 we organized two workshops on topics connected to water, supercooled water, water in confinement and aqueous solutions. A special issue of the Journal of Physics: Condensed Matter, edited by us, was associated to the first workshop . Both workshops were most successful and stimulated a great interest in the field in the following years. Participants of the workshops were enthusiastic and the vivid discussions done in these CECAM workshops contributed to big steps forward done in this field. We add that this workshop format, perfectly organized and supported by CECAM, proved to be ideal for this kind of topics and the community we are addressing to.
We want to focus, in this new workshop to be held in 2013, mainly on the very recent debate on water polyamorphism, nucleation, glassy behaviour and liquid-liquid critical point.
As we explain below in the state of the art section, recent experimental results, computer simulations and theoretical approaches gave new insights in the understanding of the supercooled water phenomenology, and the interlink among theory, simulations and experiments has become more and more important in these last years.
We think that we are at a turning point where the different methods appropriately combined can address toward the final understanding of many of the anomalies of water. For this reason we decided to propose this new workshop where also experimentalists will be invited among our speakers, since it is very relevant to have a confrontation between the different experimental, computational and statistical mechanics methods.
In the past years several theoretical and computer simulation studies have hypothesized possible scenarios to explain the thermodynamic and dynamic anomalies of water in the supercooled region .
Based on computer simulation results obtained with the ST2 water model [3,4] the anomalous behaviour of thermodynamical response functions in supercooled water was attributed to the possibility that water upon supercooling shows a liquid–liquid (LL) coexistence terminating in a liquid–liquid critical point (LLCP). This interpretation is an alternative to other hypotheses, such as the singularity free scenario .
Computer simulations also show evidence for a liquid–liquid transition in systems such as silicon [6–9] and silica [10-13]. In these cases, as in water, the phenomenon would take place in the metastable phase of the supercooled liquid, if the formation of the stable crystalline phase can be avoided. The hypothesis of a metastable LLCP in water is supported by the experimental determination of different coexisting phases of glassy water, the so-called polyamorphism of water. The high density amorphous (HDA) and low density amorphous (LDA) phases would transform at increasing temperature in the corresponding high density liquid (HDL) and low density liquid (LDL) phases [1,14]. In the metastable liquid the coexistence curve would terminate at a critical point. A first-order phase transition among HDA and LDA has been determined by experiments [15–18], while LDL and HDL are in the region of temperature and pressure hampered by crystallization. In spite of this, experimental indications of the existence of LLCP in supercooled bulk water have been found [19-20]. In particular the LLCP was hypothesized to be located at about 220 K and a pressure of 100 MPa.
After the first computations with the ST2 model a number of computer simulations have been performed with different classical model potentials to determine the LDL–HDL transition. These calculations were mainly based on the study of the equation of state (EOS) in canonical or isothermal-isobaric simulations in finite size systems upon supercooling, see for instance [21-23] including the simulation with the TIP4P/2005[24-25]. From the EOS the position of the LLCP has been estimated in water and in other liquids with a tetrahedral structure. In computer simulations the use of small systems and short time scale could avoid the formation of a crystalline nucleus making more easy than in experiments the observation of phenomena in supercooled liquids.
The interpretations of the EOS simulated in the canonical or constant pressure ensemble were recently questioned by Limmer and Chandler . They proposed that the observed behaviour of water upon supercooling is related not to a putative LL transition but it reflects the incipient liquid-crystal transition of the LDL.
The criticism makes clear that accurate evaluations of the EOS via simulations
is necessary to locate the LLCP and the universality class of the LL critical transition. From this point of view computer simulation techniques already used to study critical phenomena need to be introduced in the field. Grand canonical Monte Carlo (GCMC) simulation with the use of histogram reweighting, umbrella sampling, finite size scaling  can play an important role in determining the existence of a LLCP in water or in other network forming liquids. Liu et al. performed the first GCMC simulation of the LLCP in ST2 water, confirming the previous EOS calculations. But Limmer and Chandler considered the Liu et al.  result as a non equilibrium phenomenon where the LDL would be not a well defined metastable state. Sciortino et al. [29-30] and Kesselring et al.  performed further very accurate and long simulations on ST2 water where they confirm the presence of a LLCP and validate for the moment the previous EOS calculations. Finite size scaling on successive umbrella sampling  GCMC simulations on spherically symmetric ramp potential particles of Jagla-type mimicking the properties of water, shows the existence of a second order LLCP that belongs to the Ising Universality class .
In the meantime it has been formulated a theory of the liquid-liquid critical phenomenon that can account for all currently available experimental data in the supercooled region of water, up to 400 MPa 
The LLCP hypothesis is controversial but it has the power to rationalize and connect thermodynamical and dynamical phenomena of supercooled water. According to theoretical and computer simulations study on bulk water a line of maxima of the correlation length, called the Widom line, is emanated from the LLCP. In crossing this line it is found a fragile to a strong crossover (FSC) in the dynamical relaxation of water in analogy with others network forming liquids . Quasielastic neutron scattering (QENS) experiments performed on supercooled water in confinement found evidence of a FSC [36-39]. Computer simulation supported the evidence of the FSC in water confined in MCM41 materials . Further experimental evidence was obtained from Nuclear Magnetic Resonance and QENS spectroscopies of a well defined decoupling of transport properties, the self-diffusion coefficient and the average translational relaxation time with a violation of the Stokes-Einstein relation in the region of the FSC [39,41].
In the natural environment water is almost ever found as a solvent in mixtures of two or more components and/or confined in different organic or inorganic substrates. Water can be more easily supercooled in solutions and indications of the possible presence of a LLCP in aqueous solutions have been found experimentally [42-45].
Recent calculations of the EOS of TIP4P water solvated in NaCl at different concentrations determined the possible existence of a LLCP [46-47]. Nonetheless the existence and the position of LLCP in the thermodynamic plane for an aqueous solution has not yet been determined in experiments.
Also the relation between the behaviour of confined water and bulk water is a matter of controversy between experimentalists .
This debate is also very important as both aqueous solutions and confined water represent viable experimental routes for the observation of the supercooled region where the LLCP is supposed to exist.