The main goal for founding the Scientific Center of Excellence for Quantum and Complex Systems, and Representations of Lie Algebras (QuantiXLie)- is to strongly reinforce the international visibility of theoretical physics and mathematics research conducted at Croatian universities and scientific institutes, ant to enable implementing large competitive projects for international programs. ZCI QuantiXLie aims to create a motivating environment for learning and training of young researchers and provide a stable long-time financial framework for their education and professional development. Members of the QuantiXLie center are internationally recognized researchers who publish their results in leading international scientific journals, which gather significant number of citations and have impact on the scientific community.

The QuantiXLie group is composed of researchers from The Faculty of Science (PMF) of the University of Zagreb (UniZG), Faculty of Electrical Engineering and Computing (UniZG), Faculty of Civil Engineering University of Zagreb (UniZG), Faculty of Metallurgy UniZG, Faculty of Textile Technology UniZG, Institute of Physics (IF), Ruđer Bošković Institute (IRB), Department of Mathematics – University of Rijeka and Faculty of Science of the University of Split (UniST). The total potential of theoretical physics and mathematics in Croatia is far from the full utilization (even though it is a less expensive research from e.g. experimental physics) with potentially large impact. There is no stable source of funding for graduate students, resulting in the number of graduate students far below the mentoring capacity of researchers. Furthermore, each group of researches is concentrated on a relatively narrow area of research while synergy potential of research groups remains unrealized. The goal of the QuantiXLie center is to remedy all these deficiencies and take full advantage of the potential of our researchers.

QuantixLie center is organised in two units: (i) Unit for Theory of Quantum and Complex Systems and (ii) Unit for Representation Theory of Lie Algebras, Number Theory, and Related Structures. In the initial phase of the implementation, the scientific program of the first unit will be focused on subjects of atomic and nuclear physics, condensed matter physics, optics and photonics as well as biophysics. The science program of the second unit can be divided in three main categories: a) Harish-Chandras modules and Dirac’s operators, b) Kac-Moody’s and Lies algebras, vertex-algebras, W-algebras and conformal field theory and c) numbers theory, elliptic curves and modular forms. QuantiXLie center will tend to adapt its researches with a goal to strengthen the synergy between groups and to provide quality project applications for further financing from international sources. After the conclusion of this five-year program, ZCI QuantiXLie will be self-sufficient and its influence should have a wider impact, even beyond the academic community. The skills our young researchers will develop through working in QuantiXLie, are extremely sought of and valued in IT, innovation and financial sectors and this is how we could accomplish an overflow of skills and knowledge even beyond the boundaries of academic community of Croatia.