Precise understanding of strongly correlated quantum matter is a major goal of modern physics**.** Complete understanding of a many-body strongly correlated system normally implies three complementary ingredients—and thus three distinct directions of research:

(i) An effective theory or a general method addressing relevant degrees of freedom and/or emergent constants of motion characteristic of a given phase of quantum matter; (ii) a possibility to trace the origin of an effective description by solving microscopic models; (iii) experimental verification of the theory at both qualitative and quantitative level. Nowadays, an impressive progress is being made along all the three directions. Non-trivial effective theories of quantum phases and phase transitions, and elegant topological methods are being developed. Breathtaking experimental achievements in the field of ultracold atoms are making feasible analog quantum simulations aimed at controllable experimental realization of key many-body quantum models. Many experimentalists working in this field are now thinking “theoretically” in terms of experimentally solving notoriously difficult Hamiltonians, such as, e.g., the repulsive fermionic Hubbard model. An exciting effort is associated with engineering novel Hamiltonians. New classes of universal first-principles approaches are being developed.

The program will bring together the world’s experts of controllable theoretical and experimental approaches. We expect that the program will substantially promote further progress in synergistically related areas of physics dealing with strongly correlated many-body quantum physics.

The key topics of the program will include exactly solvable models and first-principles numeric approaches (such as tensor network and density-matrix renormalization group methods; path-integral, stochastic-series, and diagrammatic Monte Carlo; dynamic cluster approximations, etc.); effective coarse-grained description of quantum phases and phase transitions; topological methods yielding controllable description of phases with topological order (topological insulators, fractional quantum Hall states, etc.). Of special interest will be the topic of quantum simulation with ultracold atoms as well as condensed-matter systems.

In view of crucial importance of quantum simulation and related experimental areas for the goals of the program, the last week of the program will be devoted to a symposium featuring new experimental developments on strongly correlated Bose and Fermi gases, including accurate thermodynamic measurements, lower dimensions, quantum magnetism, non-equilibrium systems, topological states of matter, graphene-like systems, artificial gauge fields and spin-orbit coupled gases, beyond s-wave interactions and few-body systems. In all these fields, breakthroughs have been achieved recently, and more are anticipated, where models from many-body physics can be tested with precision or entirely new systems are realized that still await their accurate description. With this symposium we hope to collect benchmarks for precision many-body physics and define the most urgent unsolved but tractable problems for future experiments.

**Key topics: **

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- Controlled numeric approaches and exactly solvable models

- Effective theories

- Topological methods

- Achieving quantum simulation