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Nuclear Structure Atomic nuclei, the core of matter and the fuel of stars, are self-bound collections of protons and neutrons (nucleons) that interact through forces that have their origin in quantum chromo-dynamics. Nuclei comprise 99.9% of all baryonic matter in the Universe. The complex nature of the nuclear forces among protons and neutrons yields a diverse and unique variety of nuclear phenomena, which form the basis for the experimental and theoretical studies. Developing a comprehensive description of all nuclei, a long-standing goal of nuclear physics, requires theoretical and experimental investigations of rare atomic nuclei, i.e. systems with neutron-to-proton ratios larger and smaller than those naturally occurring on earth. The main area of my professional activity is the theoretical description of those exotic, short-lived nuclei that inhabit remote regions of nuclear landscape. Key scientific themes that are being addressed by my research are captured by overarching questions: o What is the nature of the nuclear force that binds protons and neutrons into stable nuclei and rare isotopes? o What are the limits of nuclear existence? o What is the origin of simple patterns in complex nuclei? o How can our knowledge of nuclei and our ability to produce them benefit the humankind? Most of the above physics problems invite a strong interaction between nuclear physics, many-body-problem, and high- performance computing. Quantum Many-Body Problem Heavy nuclei are splendid laboratories of many-body science. While the number of degrees of freedom in heavy nuclei is large, it is still very small compared to the number of electrons in a solid or atoms in a mole of gas. Nevertheless, nuclei exhibit behaviors that are emergent in nature and present in other complex systems. For instance, shell structure, symmetry breaking phenomena, collective excitations, and superconductivity are found in nuclei, atomic clusters, quantum dots, small metallic grains, and trapped atom gases. Although the interactions of nuclear physics differ from the electromagnetic interactions that dominate chemistry, materials, and biological molecules, the theoretical methods and many of the computational techniques to solve the quantum many-body problems are shared. Examples are ab-initio and configuration interaction methods, and the Density Functional Theory, used by nuclear theorists to describe light and heavy nuclei and nucleonic matter. Physics of Open Systems Today, much interest in various fields of physics is devoted to the study of small open quantum systems, whose properties are profoundly affected by environment, i.e., continuum of decay channels. Although every finite fermion system has its own characteristic features, resonance phenomena are generic; they are great interdisciplinary unifiers. In the field of nuclear physics, the growing interest in theory of open quantum systems is associated with experimental efforts in producing weakly bound/unbound nuclei close to the particle drip-lines, and studying structures and reactions with those exotic systems. In this context, the major problem for nuclear theory is a unification of structure and reaction aspects of nuclei, that is based on the open quantum system manybody formalism. Solution of this challenging problem has been advanced recently through the new-generation continuum shell model approaches, in particular the Gamow Shell Model based on the Berggren ensemble. The recent development of the DensityMatrix Renormalization Group algorithm for open quantum systems within the rigged Hilbert space formulation of quantum mechanics, enables presently fully converged configuration interaction calculations.