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# Dyson-Schwinger Equations in Modern Mathematics & Physics

Dyson-Schwinger equations (DSEs) are ubiquitous in physics. Their most rewarding applications are found in theidentification and explanation of nonperturbative phenomena in QCD. In parallel, there has been real progress in the mathematical understanding of DSEs, with the realisation that renormalisation is naturally expressed via a Hopf algebra structure. This enables a comprehensive description of the algebraic and combinatorial structures underpinning renormalisation. Following this realisation, mathematicians have been motivated to imagine that Hopf algebra framework has the power to provide deeper insights into fundamental problems in quantum field theory. The overriding aim of this meeting is to lay the foundation for a broadly-based working group, at the interface between mathematics and physics, which can work to reveal novel methods for tackling nonperturbative phenomena in the strong interaction sector of the Standard Model.

## Organizers

Mario Pitschmann | TU Vienna | |

Wolfgang Lucha | IHEP Vienna | |

Craig Roberts | Nanjing Universiity |