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The main purpose of the conference is to stimulate and promote interactions between three major research areas: (quantum) algebra, including (quantum) geometry, (quantum) integrable models and (quantum) information theory. This conference is a satellite event to the 7th European Congress of Mathematics (ECM) in Berlin, and continues the following series of satellite conferences to the European Congresses of Mathematics: 1. Noncommutative Geometry and Representation Theory in Mathematical Physics. Satellite conference to the 4th ECM in Stockholm (2004). 2. Noncommutative Structures in Mathematics and Physics. Satellite conference to the 5th ECM in Amsterdam (2008). 3. 3Quantum: Algebra Geometry Information. Satellite conference to the 6th ECM in Krakow (2012).