Solution of Broue's conjecture in representation Theory of finite groups

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For the subject "Broue's conjecture" we have proven the following. First of all, we proved Broue's conjecture for one of the sporadic simple groups, say the Janko's simple group J4, joint work with N.Kunugi and K.Waki. Secondly, we proved the Broue's conjecture also for one of the sporadic simple groups, say Harada-Norton simple group HN, joint work with J.Mueller. We also proved a kind of tool by which we can find out trivial source modules, joint work with N.Kunugi. With M.Holloway and N.Kunugi, we proved also a theorem which was on Rouquier's conjecture. The conjecture is a kind of analogue of Broue's conjecture. Finally we proved a result on eigenvalues of the Cartan matrices of blocks of finite groups, jointly with Y.Yoshii.