Anglo-Franco-German in Representation Theory and its Applications

Representation theory is one of the most active fields of mathematics today with applications in many of the sciences and interactions with many other mathematical disciplines. This beautiful subject originated in a letter to Frobenius by Dedekind more than a century ago. Roughly speaking, Representation Theory can be thought of as the study of basic symmetries in Mathematics and Physics, symmetries that can take many forms: groups, associative algebras, Hopf algebras or Lie algebras to name a few.

A striking feature of Representation Theory is its rich history of interactions and applications to other topics in mathematics and to all sciences. For instance, in the last few years only, Representation Theory has fruitfully interacted with Geometry, Model Theory, Number Theory, Probability and Theoretical Physics to name a few. Representation Theory through its great diversity can be used to unify different themes and is currently at the heart of an intense research activity (through worldwide research programmes such as the Langlands programme).

Given this background, it is necessary to provide researchers in Representation Theory with opportunities to develop a broader vision, and for other researchers to learn about the latest developments in Representation Theory. The proposed network will serve as a catalyser to stimulate interactions between Representation Theory and other areas, through the organisation of various interdisciplinary/intradisciplinary events in a coordinated effort with researchers from France and Germany.

There are three main activities that will be carried forward during the project in order to ensure it reaches its full potential.

1) Communication and engagement. This will be achieved through the proposed conferences, courses, seminars, visits and workshops. The conference on Representation Theory and Art will open up new routes for communication and engagement activities around Representation Theory. In particular, we expect that in the medium term this might lead to new interdisciplinary research, but also new outreach activities.

2) Training. A crucial ingredient of the Network, with full impact in the medium to long term, is the provision of plentiful training in a highly interdisciplinary/intradisciplinary area. The organisation of workshops, instructional conferences and short meetings which bring together early-career researchers with established scientists from different countries and from different disciplines is key to this. These meetings will provide a vehicle to present work to a wide audience, to broaden knowledge and to establish first contacts for possible further collaborations or job applications. It will also act as a facilitator for interdisciplinary research involving Representation Theory. In particular, the Network will organise bespoke courses with CDT/Taught Course centres where Representation Theory has applications to ensure the next generation of mathematicians learn about the latest developments in Representation Theory. This will also widen the impact and visibility of these centres by giving them an international dimension.

3) Collaboration. The international component of our Network provides a unique chance to benefit from existing cultures of interdisciplinary cooperations in France and Germany, giving UK-based researchers access to intellectual and physical resources there. Strengthening collaboration with our European partners is an ideal vehicle to achieve the aim of improving the quality of PhD students and the competitiveness of early-career researchers in the international context.