Members of the Algebra Group: some thumbnail sketches
This page gives sketches of our research interests, links to our personal web pages, our author profiles in MathSciNet and our entries in the Mathematics Genealogy Project. Many of us keep details of our teaching and research on our personal web pages. The MathSciNet author profiles give access to
- up-to-date lists and reviews of our publications,
- our citation counts since 2000 with lists of most cited papers,
- our co-authors and collaboration data.
(Note that a MathSciNet subscription is necessary to access these pages.) From the Mathematics Genealogy Project you can find our mathematical ancestors and descendants.
John Bray researches finite groups and the objects on which they act, and is interested in explicit representations and presentations of groups. He also works in computational group theory. At present he classifying the maximal subgroups of the finite classical groups and their automorphism groups.
Matt Fayers works in representation theory of finite groups and finite-dimensional algebras, especially representations of the symmetric group (in prime characteristic) and related Hecke algebras. He is interested in finding decomposition numbers and the structures of modules for these algebras. This work is highly combinatorial in flavour, and Matt also works in combinatorics (especially the combinatorics of partitions) related to representation theory.
Alex Fink works in algebraic combinatorics, especially in combinatorics informed by commutative algebra and algebraic geomety. His recent work has concerned matroids, their invariants, and varieties associated to them, and tropical geometry and algebraic statistics.
Thomas Müller studies the function giving the number of subgroups of given index in a finitely generated group. He is concerned both with the growth rate of this function, and with divisibility and arithmetic properties. This work involves algebra, combinatorics, and analysis, and has implications for subjects such as Quillen complexes.
Leonard Soicher is interested in both theoretical and computational group theory, graph theory and design theory. He is closely involved with GAP, the computer system for group theory and discrete mathematics, and has developed GAP packages for studying graphs with group actions and for combinatorial design theory. These packages are widely used in the group theory and combinatorics communities. Some of the designs he has found are motivated by statistical applications. He is responsible for the website DesignTheory.org.
Robert Wilson works in finite group theory, and related areas such as representation theory, some aspects of combinatorics, and computational techniques and algorithms applicable to finite groups. He is the architect of the web-based ATLAS of Finite Group Representations, and is especially interested in the sporadic simple groups, including the (in)famous Monster group. Current interests include exceptional Lie groups and potential applications to physics.