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The first project is to publish three papers extracted from the thesis


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Research project Sebastien Palcoux 1 Immediate projects 1.1 Publication The first project is to publish three papers extracted from the thesis: Neveu-Schwarz and operator algebras III : Connes fusion and subfactors. Neveu-Schwarz and operator algebras II : Unitary series and characters. Neveu-Schwarz and operator algebras I : Vertex operator superalgebra. A big work of formatting is necessary. 1.2 Ramond case The (R) case Vir0 is more difficult for many reasons: we need to intro- duce twisted vertex module over the vacuum vertex algebra of the (NS) case Vir1/2. We need module because Vir0 doesn't admit h = hm11 = 0 for cm fixed in the discrete series (because in (R) case p? q ? 1[2]), and twisted for going from ? = 1/2 to ? = 0; the Kac determinant in (R) case introduces a new vanishing curve: h = c/24 (we call it C0); there is a hole if we want to prove the FQS criterion in a parallel way that for (NS), because the lemma 8.19 of the thesis, true for the (NS) case, is false for the (R) case: in fact, to be true, it is necessary to have Cpq ? C ?pq ? SN?1/2 with N = pq/2; it's true if q ≤ p+ 1 and false in general if q > p+ 1 (in (NS) case, it's also true thanks to the curves h =

  • operator algebras

  • string theory

  • iii1 factors

  • theory admits

  • vacuum vertex

  • krichever-novikov algebra

  • riemann surface

  • many reasons

  • vertex



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