VISITING PROFESSOR Jordan François is a mathematical and theoretical physicist who obtained his PhD from Aix-Marseille University (France) in 2014. He has held several research positions: as a Riemann Fellow at the Riemann Center for Geometry and Physics in Hannover (Germany) in 2015; as an FNRS Postdoctoral Researcher in the Department of Physics, within the Physics of the Universe, Fields and Gravitation group, at the University of Mons (Belgium) from 2018 to 2021; as an MSCA Fellow in the Department of Mathematics and Statistics at Masaryk University in Brno (Czech Republic) from 2022 to 2024; and currently as an FWF Postdoctoral Researcher in the Department of Philosophy of Science at the University of Graz (Austria), where he will remain until 2028. He taught as a doctoral candidate and subsequently as a teaching assistant in the Departments of Physics and Mathematics at Aix-Marseille University from 2011 to 2015, and as a teaching assistant at the Institut Élie Cartan in the Department of Mathematics at the University of Lorraine in Nancy (France) during the 2017–2018 academic year. He also taught an advanced second-year Master’s course for physics and mathematics students at the University of Mons from 2019 to 2021. He has co-supervised three Master’s theses and three doctoral candidates in the Physics Departments of the Universities of Marseille and Mons. He has also delivered lectures for doctoral and postdoctoral researchers at the 2021 Modave Summer School (Belgium) and at a specialised conference and school held in Turin (Italy) in 2026. His research focuses on the mathematical and conceptual structure of generally relativistic gauge field theories. His work lies primarily in the field of mathematical physics and also includes publications on the philosophy of physics and local symmetries. -Our two most successful theories of fundamental theoretical physics, both supported by overwhelming empirical evidence, are General Relativity (GR) and the Standard Model (SM) of particle physics. Together, they constitute the foundational framework of general-relativistic gauge field theory (gRGFT). Mathematically, this framework is based on the differential geometry of connections on fibre bundles, a field that has been fully developed since the early 1960s, precisely when the Standard Model was taking shape.

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Following a brief historical overview of the origins of gauge field theory and the line of influence leading from General Relativity to the modern theory of connections, the course will provide a systematic introduction to the mathematical foundations of general-relativistic gauge field theory. Particular emphasis will be placed on a clear logical and conceptual presentation of its key notions. The course will also introduce new material, not yet available in textbook form, concerning cocyclic geometry on field space. Finally, it will highlight the profound conceptual implications of local symmetries—diffeomorphisms and gauge symmetries—for our understanding of the nature of spacetime and fundamental fields, as implicitly suggested by general-relativistic gauge field theory.

In presenza

Presentazione orale - Presentazione report scritto

P.D.2-2 - Settembre