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Universität Augsburg
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Universität Augsburg
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Dr. Kazuki Kudomi
Tohoku University, Japan
spricht am
Dienstag, 7. April 2026
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10:00 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| This talk is an exposition of our preprint, “A Morse Theoretical Approach to Fourier Transforms of Holonomic D-Modules in Dimension One,” joint with Kiyoshi Takeuchi (Tohoku University). Based on the formalism of enhanced ind-sheaves and D’Agnolo-Kashiwara’s Riemann–Hilbert correspondence, we study Fourier transforms of holonomic D-modules on the complex affine line. As a result, we obtain characteristic cycles of Fourier transforms of holonomic D-modules and give a new proof of the stationary phase formula. The first crucial step in the proof is to construct an enhanced sheaf such that it is isomorphic to each enhanced solution complex after convolution. The second key step is the use of Morse theory in a situation where several Morse functions appear. One aim of this talk is to make our proof accessible to the audience. For a meromorphic connection on the complex affine line, we can construct a not necessarily conic Lagrangian cycle, called the irregular characteristic cycle, which encodes its formal structure. We will also explain how the stationary phase formula can be understood as the symplectic transform of this cycle. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Marco Hien |