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12 Jul 2011: Representation Theory. Lectured by S. Martin. Lent Term 2009, 2010, 2011. 1 Group Actions 1. 2 Linear Representations 3. 3 Complete Reducibility and Maschke’s Theorem 7. 4 Schur’s Lemma 10. 5 Character Theory 13. 6 Proofs and Orthogonality 17. 7

6 Jul 2011: 1. Pedley TJ, Kessler JO (1992) Hydrodynamic phenomena in suspensions of swimmingmicroorganisms.

10 Apr 2011: Continuum theory of critical phenomena in polymer solutions: Formalism and mean field approximation. Raymond E. Goldstein Laboratory of Atomic and Solid State Physics and Materials Science Center, Clark Hall, Cornell University, Ithaca, New York

15 Sep 2011: In a similar manner as in the proof of Theorem 2, we have that for s = o-i and t = Tj,. ... T'E4 (X('Tj) E (Nk (st) -Nk (S))t). and therefore E(vi) is o(t).

1 Sep 2011: The subintervals of and their lengthes will be denoted by. Ij := (tj, tj1), |hj| := tj1 tj. ... Nj = 1, (1.1.1). Mj (x) =k. tjk tjNj(x),. tjk. tj.

10 Apr 2011: tJ.Se(T,Hcrit ) = Se(T,H--Hcrit ) - Se(T,H--Hcrit -). (17). where.tJ.Ms is the order parameter jump of the SM. ... tJ.Me(T ,Hcrit) = Me(T ,H--Hcrit ) - Me(T ,H--Hcrit -). (18).

14 Nov 2011: 25. . Theorem 5.8. Suppose P is irreducible and recurrent.Then for all j I we have P(Tj < ) = 1.

18 Sep 2011: Pij (J1) = P { i K (tJ ) -] = j L1 i < j 1, pEA,.

24 Jan 2011: tr](this means that σ is a product of disjoint cycles of length t1 > > tr where n = t1 tr,and some of the tj may be equal to 1.

15 Nov 2011: 3) Let Tj be the jth Chebychev polynomial. Suppose γj is a sequence of non-negative numberswith.