Quarks are elementary particles that are strongly bound inside protons and neutrons. The residual strong interactions between protons and neutrons give rise to all of nuclear physics, from the simplest nuclear reactions responsible for fusion, to the intricate structure of large unstable nuclei. In essence, nuclei are to the strong 'chromodynamic' force what molecules are to the electromagnetic force. Tremendous progress is being made by solving the theory of strong interactions numerically. Current computing power and algorithms have put one within reach of realistic computations. Quantitative knowledge of the strong force will ultimately render nucleons and nuclei into laboratories for investigating fundamental symmetries and probing the limits of the Standard Model of particle physics. The comprehensive research program of the PI will combine advances in theoretical physics and high-performance computing to help advance our knowledge about nucleons and nuclei to the most advanced level yet. Moreover, the scope of this program affords both student and post-doctoral researchers considerable opportunities for training in nuclear and computational science, two areas in which an advanced technical workforce is much needed.The scientific goal of this project is to study electromagnetic and parity-violating properties of strongly bound systems directly from Quantum Chromodynamics (QCD). The distribution of charge and magnetism within nucleons will be explored by calculating their magnetic moments and electromagnetic polarizabilities using lattice gauge theory. Effort will also be geared toward studying the electromagnetic structure of light nuclei and hyper-nuclei using lattice QCD techniques, including the challenge of reducing the quark mass. Manifestations of the weak interaction at low energies will additionally be investigated from QCD. The parity-violating component of non-leptonic weak interactions introduces hadronic parity violation, and probes quark-quark correlations deep within hadrons. Due to feasibility of lattice QCD computations in the isotensor channel, lattice renormalization of isotensor parity violation will be determined and electromagnetic mixing will be addressed for the first time. Novel methods will be sought for future lattice calculations in the remaining isospin channels.