Generalized Quatum Batalin-Vilkovisky Formalism and Graphical Calculus

One of the greatest successes of physics is the quantum field theory (QFT), with its stunningly accurate predictions. These are usually obtained by drawing so-called "Feynman diagrams". In this fellowship, I will develop new methods to obtain and manipulate these diagrams, achieving the following two objectives: The first objective is a generalization of the Batalin-Vilkovisky approach to QFT using ideas from symplectic geometry and operads. The outcome will be a category of operadic Batalin-Vilkovisky theories and generalized Lagrangian relations between them, together with a set of interesting examples and applications to topological recursion. This will be a common generalization of the ideas of Barannikov on modular operads and Batalin-Vilkovisky formalism, and the ideas of Ševera on the quantum odd symplectic category. The second objective is to develop computer assistant for graphical calculus, or an "intelligent paper". This will be an app allowing the user to perform calculations with string diagrams for symmetric and braided tensor categories, bringing the formalism introduced by Penrose to the computer screen. This will be a strongly interdisciplinary fellowship, combining mathematical research related to physics with applied computer science. Strong dissemination activities are planned to promote the app for graphical calculus, including a secondment at the School of Informatics at the University of Edinburgh, a leading research institute for quantum computing. At the Departments of Mathematics and Physics of the Humboldt University in Berlin, I will benefit from the active scientific environment and the expertise of my supervisor and co-supervisor. Their mentoring and the fellowship will develop my skills in mathematics, teaching, event organization and dissemination, allowing me to establish myself as a researcher.