

1st year tutor  
My main administrative role within the School is that of 1st year tutor, with oversight of 1st year undergraduate students.  
59 September, 2016 Morita equivalence problems for blocks of finite groups, workshop forming part of the semester Local representation theory and simple groups at the Centre Interfacultaire Bernoulli, EPFL, Lausanne. 

I am organising this workshop along with Michael Livesey. If you are interested in coming, or giving a talk, then please contact me or Michael.  
Research  
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 2blocks 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 2groups, examination of Loewy lengths and understanding Galois conjugacy of blocks.  
Teaching  
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 psolvable groups  
Recent papers  
(with M.Livesey) Loewy lengths of blocks with abelian defect groups, submitted Morita equivalence classes of $2$blocks of defect three, Proc. AMS 144 (2016), 19611970 (with R. Kessar, B. Külshammer and B. Sambale) $2$blocks with abelian defect groups, Adv. Math. 254 (2014), 706735 (with A. Moreto) Extending Brauer's height zero conjecture to blocks with nonabelian defect groups, Int. Math. Res. Not. 2014 (2014), 55815601.(available electronically) (with J. An) Nilpotent blocks of quasisimple groups for the prime two, Alg. Rep. Theor 16 (2013), 128 (with B. Külshammer and B. Sambale) $2$blocks with minimal nonabelian defect groups, II, J. Group Theory 15 (2012), 311321. (with J. An) Blocks with extraspecial defect groups of finite quasisimple groups, J. Algebra 328 (2011), 301321 (with D.Craven, R.Kessar and M.Linckelmann), The structure of blocks with a Klein four defect group, Math. Zeit. 268 (2011), 441476 (with J. An) Nilpotent blocks of quasisimple groups for odd primes, J. Reine Angew. Math. 656 (2011), 131177 
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