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Pin-Hsun Chuang (NTU)
2025-11-03  11:40-12:30
Room 202, Astronomy and Mathematics Building

In SGA 7 II, Deligne established the Picard–Lefschetz formula describing the action of the inertia group on the vanishing cycles of a proper flat family X → R over a Henselian discrete valuation ring R whose special fiber has only isolated ordinary quadratic singularities. In this talk, I will present a generalization of this formula to families whose special fibers have isolated singularities of type A_k. Moreover, I will give an explicit description of the inertia group and Frobenius actions on the vanishing cycles in the case of A_2-type singularities. Finally, I will briefly discuss how these results provide new insights into the study of the arithmetic aspects of Airy-type differential equations with irregular singularities.