{"id":1078,"date":"2019-01-08T10:22:16","date_gmt":"2019-01-08T10:22:16","guid":{"rendered":"http:\/\/blogs.kent.ac.uk\/smsasnews\/?p=1078"},"modified":"2019-01-09T14:36:02","modified_gmt":"2019-01-09T14:36:02","slug":"bas-lemmens-celebrates-epsrc-funding-award","status":"publish","type":"post","link":"https:\/\/blogs.kent.ac.uk\/smsasnews\/bas-lemmens-celebrates-epsrc-funding-award\/","title":{"rendered":"Bas Lemmens celebrates EPSRC funding award"},"content":{"rendered":"

Reader in Mathematics, Dr Bas Lemmens\u2019 award from the Engineering Physical Sciences Research Council (EPSRC) is for a three-year project investigating the deep seeded interplay between geometry, order structures, and Jordan algebras. Bas is working with Professor Cho-Ho Chu at Queen Mary University London. <\/span><\/p>\n

Bas outlined the nature and scope of the project for us. \u2018The notion of a Jordan algebra has a rich history in mathematics. It was originally introduced by Pascual Jordan in a quest to find alternative algebraic settings for quantum mechanics and turned out to have deep connections with diverse areas of mathematics including Lie theory, differential geometry and mathematical analysis. A beautiful connection between finite dimensional Jordan algebras and the geometry of cones was discovered by Koecher and Vinberg. Their characterisation of finite dimensional Jordan algebras provides a link with the geometry of Riemannian symmetric spaces. One of the main aims of the project is to establish similar characterisations of Jordan algebras in infinite dimensional spaces. There is some evidence that Jordan algebra structures are closely related to a certain symmetry of order structures coming from cones. Indeed, it is believed that the existence of a transformation on the cone that reverses, ie, flips, the order structure implies the existence of a Jordan algebra structure on the space. It would be really exciting to prove this striking connection. <\/span><\/p>\n

\u2018There are several paths to follow and avenues to explore. As with all research, we can\u2019t predict the outcome but it\u2019s an exciting project, building on fundamental work of the past, such as that of Koecher and Vinberg, and the knowledge gained since, to further our understanding of this fascinating research area and hopefully discovering something that moves the field in new directions<\/span>.\u2019<\/span><\/span><\/p>\n