Applications of curved Yang-Mills-Higgs theories

• Applicant: Dr. Simon-Raphael Fischer
• Subject Area: Mathematics ; Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 579748104

My major research focus concerns curved Yang-Mills-Higgs theories, also sometimes called curved gauge theories, and their applications; for example, tools of curved gauge theories help to classify singular foliations, and in return the study of singular foliations helps to construct new gauge theories which cannot be described in an ordinary way. Besides singular foliations, we pointed out that one can classify patterns of the Higgs mechanism for scalar vacuum expectation values, and currently I am developing an obstruction theory for a certain kind of short exact sequences of bisubmersions, making use of the Atiyah sequence of curved Yang-Mills-Higgs theories, and this leads to a generalisation of short exact sequences of Lie algebroids providing a topological invariant and giving further hints about the structure of Lie algebroids equipped with a Cartan connection. Besides that, we are currently extending our classification of singular foliations to Lie groupoids and related structures, and we are investigating the total space description of curved Yang-Mills-Higgs theories for new examples and further applications.

• DFG Programme: Position