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The Banff International Research Station will host the "Charge and Energy Transfer Processes: Open Problems in Open Quantum Systems" workshop in Banff from August 18 to August 23, 2019. We seek to bring together leaders from the Mathematical Physics and Chemical Physics communities who are interested in the theory of open quantum systems dynamics with a focus on charge and energy transfer dynamics in condensed phases systems. Participants have research expertise in analytical and computational method development in the fields of mathematical physics, chemical dynamics, quantum decoherence, dissipation and transport, quantum thermodynamics, quantum statistical mechanics, and quantum many-body physics. The overarching goal of the workshop is to open the dialog between mathematicians, physicists and chemists, to identify the important open theoretical problems surrounding transfer processes and to craft solution strategies. The workshop helps breaking ``language barriers" which prevent mathematicians from applying their knowledge to relevant chemistry problems and which prohibit chemists from applying new mathematical tools. The idea is to join research efforts of different communities working on similar problems, with the long term goal of creating collaborations, ultimately delivering mathematically rigorous results for realistic systems relevant to physics and chemistry. Specific topics and questions discussed at the workshop are: Markovian and nonmarkovian quantum master equations. Analyze their microscopic derivations, their limitations and potential rigorous perturbative extensions. What are the parameter regimes relevant in chemical physics, including biological systems, for which a mathematical treatment is needed (time scales, interaction strengths, complexity, size of the systems)? Quantum statistical mechanics and irreversible dynamics. Explore the mathematical framework of quantum statistical mechanics, with particular focus on the dynamics of decoherence, relaxation, charge and energy fluxes and their fluctuations. Identify key issues which require mathematical attention. What are models and phenomena in chemical physics that defy an uncontroversial analytical or numerical treatment? Can the current mathematical methods be applied/extended to remove controversy? Non-equilibrium behaviour in quantum many-body system. Discuss quantum impurity models central to chemical dynamics. Consolidate physical and mathematical questions. Scrutinize theoretical frameworks, numerical techniques and computational implementations. Which are the problems the chemical physics community would like to see solved in a mathematically rigorous manner? The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada-s Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta-s Advanced Education and Technology, and Mexico-s Consejo Nacional de Ciencia y Tecnología (CONACYT).