【114/5/1】16:20-17:10 Colloquium：Prof. Jen Chieh Hsiao (Department of Mathematics, National Cheng Kung University))
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| Date | 2025-5-1 16:20-17:10 |
| Place | Mathtmatics Building 1F Classroom 3173 |
| Speaker | Prof. Jen Chieh Hsiao (Department of Mathematics, National Cheng Kung University)) |
| Title | MONODROMY CONJECTURE/ HILBERT SCHEMES/ WEYL ALGEBRAS |
| Abstract | The talk consists of a brief overview of the following topics. (1) After introducing Denef–Loeser’s motivic monodromy conjecture, I will explain how one can extend the conjecture to the case of normal toric varieties. This is partly based on the joint works with Matusevich and Lai. In particular, it is proved that the conjecture holds true for monomial ideals on smooth toric varieties, but fails in general. The three key notions in this story are the motivic zeta functions, Milnor fibrations, and Bernstein–Sato polynomials. In the discussion, I will also mention an extension of a result of Denef–Loeser, expressing the Lefschetz number of Milnor monodromy as the Euler characteristic of certain space of jets. (2) The classical Hilbert scheme parametrizes closed subschemes of projective spaces. I will explain briefly how one can use a description due to ADHM and Szendr˝oi to study singularities of the Hilbert scheme of points on affine three space. Moreover, I will also mention that the techniques of Haiman–Sturmfels’ multigraded Hilbert schemes can be applied to obtain an analogous scheme structure on the space that parametrizes admissible left ideals of the Weyl algebra. (3) If time permits, I will discuss two more results for the Weyl algebra D. The first one establishes a notion of tropicalization for left D-ideals, that is analogous to the construction in classical tropical geometry. The second, based on joint work with Lin, discusses a Cohen–Macaulay type condition on left D-modules, equipped with examples of certain GKZ hypergeometric D-modules. |
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