Charles Eaton

Charles Eaton


School of Mathematics, Alan Turing Building
University of Manchester
Oxford Road,
Manchester, M13 9PL, UK

Room 2.214
Tel: +44 (0)161 3063697
Fax: +44 (0)161 3063669

Office Hours: Tuesdays 11:30-12:30

1st year tutor
My main administrative role within the School is that of 1st year tutor, with oversight of 1st year undergraduate students.
Representation theory of finite groups, especially modular representation theory.
My main focus at the moment is on Donovan's conjecture and the classification of Morita equivalence classes of blocks of finite groups. Because of work with Kessar, Külshammer and Sambale, Donovan's conjecture is know for 2-blocks with elementary abelian defect groups, that is, there are only finitely many Morita equivalence classes of such blocks. This opens the question of classifying the Morita equivalence classes, and this has now been achieved for defect groups of order 4 (Erdmann, Linckelmann), 8 (see below) and 16 (in preparation). Classifications for larger defect groups seem possible. Related problems include the verification of Donovan's conjecture for arbitrary abelian 2-groups, examination of Loewy lengths and understanding Galois conjugacy of blocks.
MATH10111 Foundations of Pure Mathematics B.
Research students

Cesare Ardito

Elliot Mckernon

Inga Schwabrow (completed 2016) The centre of a block

Pornrat Ruengrot (completed 2011) Perfect isometry groups for blocks of finite groups

Stavros Apostolou (completed 2009) Generalisations of the representation theory of p-solvable groups

Recent papers

(with M.Livesey) Loewy lengths of blocks with abelian defect groups, to appear, Proc. AMS

Morita equivalence classes of $2$-blocks of defect three, Proc. AMS 144 (2016), 1961-1970

(with R. Kessar, B. Külshammer and B. Sambale) $2$-blocks with abelian defect groups, Adv. Math. 254 (2014), 706-735

(with A. Moreto) Extending Brauer's height zero conjecture to blocks with nonabelian defect groups, Int. Math. Res. Not. 2014 (2014), 5581-5601.(available electronically)

(with J. An) Nilpotent blocks of quasisimple groups for the prime two, Alg. Rep. Theor 16 (2013), 1-28

(with B. Külshammer and B. Sambale) $2$-blocks with minimal nonabelian defect groups, II, J. Group Theory 15 (2012), 311-321.

(with J. An) Blocks with extraspecial defect groups of finite quasisimple groups, J. Algebra 328 (2011), 301-321

(with D.Craven, R.Kessar and M.Linckelmann), The structure of blocks with a Klein four defect group, Math. Zeit. 268 (2011), 441-476

(with J. An) Nilpotent blocks of quasisimple groups for odd primes, J. Reine Angew. Math. 656 (2011), 131-177



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