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Author |
|
| Name | Martin, Benjamin |
| Research field | Mathematics |
| Career stage | professor |
| Home university/institution | University of Aberdeen, Scotland, UK |
| Department/Research unit at home university/institution | - |
| Chair/Working group at home institution | - |
International activity |
|
| Country | Germany |
| Location | Bochum |
| University | Ruhr-Universität Bochum (RUB) |
| Fund Research School | VIP |
| Type of activity | research stay |
| Period |
starts 01-01-2017 ends 31-12-2019 |
| Keywords | - |
| Report |
First VIP Visit to the RUB (March 1st until April 13th, 2018): The RUB Research School VIP grant allows Prof. Ben Martin (University of Aberdeen) to support the research training of Ms Maike Gruchot and Mr Falk Bannuscher, who are PhD students of Prof. Gerhard Röhrle. Prof. Martin will also interact with Prof. Röhrle’s wider research group, which includes several postdoctoral fellows. Prof. Martin and Prof. Röhrle have a long-standing collaboration on the geometry of algebraic groups, together with Dr Michael Bate (University of York). Group theory is the abstract theory of symmetry; it has many applications to physical sciences and other branches of mathematics. When the symmetries of a physical system are linear in an appropriate sense, the symmetries can be described using matrices. Matrix groups are important not only in their own right, but because they provide a tool for understanding more general kinds of group via the formalism of representation theory. Algebraic groups are matrix groups of a particular type; their study combines ideas from group theory/algebra with techniques from geometry. December 2017: Prof. Martin visited Bochum for first discussions with Ms Gruchot and Mr Bannuscher. The students discussed their work and Prof. Martin suggested some other research directions for them to follow. One afternoon during the visit a small workshop was held; Prof. Martin gave one of the talks. Dr Bate also visited Bochum and he, Prof. Martin and Prof. Röhrle continued their research. April 2018: A week-long Spring School on Complete Reducibility was held in Bochum: https://www.ruhr-uni-bochum.de/ffm/Lehrstuehle/Lehrstuhl-VI/springschoolcompletereducibility.html The workshop was aimed at junior researchers, including PhD students. Prof. Martin delivered six one-hour lectures, supplemented by two one-hour discussion/exercise sessions. The lectures gave an introduction to the theory of complete reducibility, but also included some more advanced material for those - such as Ms Gruchot and Mr Bannuscher - who had already encountered the subject. The second half of the Spring School consisted of five research seminars, given by Prof. Martin, Ms Gruchot, Dr Bate and two other speakers. There were over twenty participants, mostly from Germany but also from Belgium, Switzerland and the UK. There was plenty of time for participants to talk with each other outside the formal programme and there were some lively discussions. We are grateful to the Faculty of Mathematics at RUB for providing the funding that allowed this successful event to take place. During the week Prof. Martin, Prof. Röhrle and Dr Bate carried out research with Dr David Stewart (University of Newcastle, UK). Second VIP Visit to the RUB July/August, 2018: July/August 2017: Prof. Martin visited Bochum for discussions with Ms Gruchot and Mr Bannuscher. Ms Gruchot has written a preprint with Prof. Röhrle and Dr Alastair Litterick (University of Bochum). It builds on earlier work by Martin, Röhrle and Dr Rudolf Tange (University of Leeds) on relative complete reducibility for algebraic groups. The preprint already contains a number of new results but Prof. Martin suggested some different directions to explore. Mr Bannuscher is working on some problems arising from a recent paper by Martin, Röhrle, Dr Bate and Dr Stewart, concerning pseudo-reductive groups and their geometric unipotent radicals. This project will involve a mixture of theoretical arguments and concrete calculations with matrices. Prof. Martin and Prof. Röhrle continued their research on the geometry of spherical buildings. This particular piece of work, which has been ongoing for several years now, is nearing completion; the aim is to reduce a very general open problem - the Strong Centre Conjecture for spherical buildings - to a special case (“spherical buildings of type A”). The next step in our programme will be to tackle the type A case. This research is joint with Dr Bate. |