The Earth's core, the most remote and dynamic part of our planet, is composed of liquid iron alloys solidified at its center. The nature and dynamics of the core are closely related to manifold geophysical problems such as the driving force of mantle convection, the geodynamo, and planetary evolution. The core is predominantly iron (Fe) alloyed with 5-10% nickel (Ni) and some lighter elements, such as sulfur (S), silicon (Si), carbon (C), oxygen (O), and hydrogen (H). The knowledge of the properties of Fe-rich alloys and liquids under relevant core conditions is a prerequisite for understanding the composition, thermal state and dynamics of the core. In comparison to crystalline iron alloys for the inner core, there exists a remarkable lack of data on liquid properties of iron-rich alloys due to experimental challenges, which have been investigated at conditions far below those expected for the outer core. The lack of data on liquid properties and great challenges facing experimental investigations under relevant core conditions are expected to continue in the foreseeable future. This prompts the team to adopt a synergistic approach by integrating experiments at experimentally-achievable pressures with computations up to core conditions.  The focus of this collaborative research will be on the elastic and viscoelastic properties of Fe-Ni-C liquids under high pressures through the synergy between experiment and theory. This approach for investigating liquid properties represents a potential methodology for studying liquid properties under extreme conditions, so as to speculate on the suitability of such combined efforts for similar high-pressure liquid state physics research. The proposed research offers a unique opportunity to engage graduate and undergraduate students to utilize state-of-the-art experimental techniques and computational tools at multi-scale facilities (departmental, university, and national laboratory) for solving fundamental problems in an active research area.The elastic and viscoelastic properties of Fe-Ni-C liquids will be investigated at high pressures by experimental techniques such as X-ray absorption, ultrasonic interferometry, X-ray diffraction, and X-ray viscometry, in combination with computational techniques, to establish a comprehensive mineral physics database on the density, sound velocity, viscosity, and structure of the liquids in a previously uncharted pressure-temperature-composition sector. The laboratory data will provide an important foundation on which the interpretation of ultrahigh pressure laboratory data and theoretical data will be based. The low-pressure data will be used to benchmark and validate results from theoretical calculations at low-pressure, and the higher-pressure calculation results will be used to estimate and predict liquid properties under core conditions. Such a methodology largely eliminates errors often induced in long extrapolations from low-pressure to core pressures, and identifies prospective biases in theoretical calculations. High pressure-temperature behaviors of the iron-rich liquids by the synergistic efforts from laboratory experiments and theoretical calculations will help improve our understanding of the physics and chemistry of the core. Stringent tests of carbon-rich core composition models for the outer core will be performed based on the liquid properties determined from this research. The outcome of the proposed projects, i.e., structure, density, sound velocity, and viscosity of core materials, will become essential parts of the study on carbon reservoirs and deep carbon cycle in the Earth and planetary interiors. The new experimental data could also be readily used in the discussion of planetary cores, such as the lunar core. The team is committed to disseminating the results through peer-reviewed journal publications and to publicizing their work to their local and greater communities through news releases, public lectures, and their research websites.