I am a Professor of Pure Mathematics and an ARC Australian Professorial Fellow in the School of Mathematics and Statistics at the University of Sydney.

APM
Andrew Mathas
School of Mathematics and Statistics F07
University of Sydney, NSW 2006.
Australia
Office   Carslaw 718
+61 2 9351 6058 (W)
+61 2 9351 4534 (Fax)
andrew dot mathas at sydney dot edu dot au
Curriculum vitae


Research Interests

The representation theory of the symmetric groups, and the closely related cyclotomic Hecke algebras of type A, was transformed when Brundan and Kleshchev's discovered of a grading on these algebras following work of Khovanov-Lauda and Rouquier. The graded theory is harder than the "classical" approach to this subject but it reveals deeper underlying features of the representation theory which we could not see before. The underlying problems are still the same - we want to compute the (graded) dimensions and the (graded) decomposition numbers of these algebras - but there is now more structure to work with. There are indications that this new perspective may furnish us with the tools to finally answer these questions. This theory is intimately connected with the representation theory of affine Hecke algebras and quantum groups; there are also ramifications for the representation theory of the symmetric groups and finite reductive groups.

Other active interests include:

I am a member of the Algebra research group.


Publications

Alex and Erika (joint with M.)

Alex Erika

Preprints -- or see the arXiv and MathSciNet

Book

Papers

The versions on the arXiv may differ slightly from the published articles.

 

 

Code

I am one of the developers for the Sage-combinat group, an open-source platform for computer calculations in algebraic combinatorics, which is part of the Sage project.

I have contributed to the Gap 3 project, including to chevie. (I have to confess that I never liked Gap 4 so I have never used it. As Gap4 is not backwardly compatible my code does not run on it.) The following programs are included in Gap 3.4.4, which can be downloaded from Jean Michel's Gap 3 distribution.


Some mathematics links

Mathematics preprint archives


If I were a Springer-Verlag Graduate Text in Mathematics, I would be J.-P. Serre's Linear Representations of Finite Groups.

My creator is a Professor at the College de France. He has previously published a number of books, including Groupes Algebriques et Corps de Classes, Corps Locaux, and Cours d'Arithmetique (A Course in Arithmetic, published by Springer-Verlag as Vol. 7 in the Graduate Texts in Mathematics).

Which Springer GTM would you be? The Springer GTM Test