Groups of Lie Type and their Geometries

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They are primarily involved with the conjectures of Alperin, Broue and Dade in the theory of "modular representations" of finite groups.

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Professor Boltje also works in the area of algebraic number theory, where he has developed functorial methods to understand Galois actions on rings of algebraic integers in number fields. Bruce Cooperstein studies finite groups of Lie type, in the context of finite geometries geometries with a finite number of points and lines and combinatorics. Martin Weissman's research involves the interaction between representation theory, geometry, and number theory.

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Specifically, he works on automorphic forms and representations, and what is generally known as the Langlands program. Within the Langlands program, he is interested in modular forms on exceptional groups, representations of p-adic groups, and L-functions.

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Course texts are provided by the library and there are no additional compulsory costs associated with the module. Undergraduate Postgraduate taught Postgraduate research Foundation Years Pre-sessional English language courses How to apply Clearing Free online learning Continuing professional development Prospectuses.

Module Overview This is a compulsory lecture module for MMath students in their fourth year. Aims and Objectives Learning Outcomes Knowledge and Understanding Having successfully completed this module, you will be able to demonstrate knowledge and understanding of: Understand the concept of a differentiable manifold Understand the basic results of calculus on manifolds Subject Specific Intellectual and Research Skills Having successfully completed this module you will be able to: Be able to calculate the integral curve of a vector field and the Lie bracket of a pair of vector fields Calculate the connection and curvature of a metric on a manifold Subject Specific Practical Skills Having successfully completed this module you will be able to: Find infinitesimal isometries of simple metrics.

Teaching and learning methods Lectures, private study. Manifords and Differential Geometry.

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A Course in Differential Geometry. Presently he is interested in some foundational questions about automorphic L-functions, interactions between algebraic deformation theory and representations of p-adic groups, and some aspects of Iwasawa theory applied to modular forms.

Hirotaka Tamanoi works on ideas in algebraic topology inspired by constructions in mathematical physics. His work has ranged from elliptic cohomology which was given a major impetus by the work of Witten on the relation of the elliptic genus to string theory to Sullivan's string topology.

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Chongying Dong and Geoffrey Mason work in the area of vertex operator algebras. This area has its origins in two-dimensional conformal quantum field theory, and has had important applications to areas of mathematics as far a field as the theory of finite groups and the invariants of knots and of three-manifolds, as well as with topics such as elliptic cohomology, Hopf algebras and tensor categories, Kac-Moody Lie algebras.

They run, with Professor Boltje, the very active Algebra seminar in the department.