I would like to give an introduction to Saito's theory of primitive forms. First, I would like to explain the general framework: family of functions, modules of formal oscillatory integrals, higher residue pairing. Then I would like to continue with the definition of a primitive form and the construction of a Frobenius manifold from a primitive form. Proving the existence of a primitive form in the most general settings is in general a difficult open problem. I would like to give a proof of the existence of a primitive form in the case of weighted-homogeneous singularities. My argument will be very pedagogical, relying on results from standard textbooks only.

Finally, I would like to discuss the period map defined by the primitive form in the settings of weighted-homogeneous singularities. More precisely, I am interested in the problem of finding the image via the period map of the set of vanishing cycles. I would like to formulate the problem precisely and to give an account of what is known.

要申込: 11 月 8 日（水）締切厳守!
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