Seminar za dinamičke sustave

U srijedu, 28.10.2026., u 16:15, u predavaonici A001, Jesús Alberto Palma Márquez (UNAM) održat će predavanje:

"Newton Polygons, Holonomy, and Integrability of Holomorphic Foliations".

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On Wednesday, 28/10/2026 at 16.15, at Faculty of Science, Dept of Mathematics, Room A001, Jesús Alberto Palma Márquez, UNAM, will give a talk:

"Newton Polygons, Holonomy, and Integrability of Holomorphic Foliations".

Abstract:
In this talk, we discuss the existence of holomorphic first integrals for germs of singular holomorphic foliations in the complex plane, from the viewpoint of Newton polygons and toric resolutions.

Under suitable nondegeneracy and convenience assumptions, we investigate holomorphic integrability through the holonomy of a distinguished component of the exceptional divisor. Focusing on Newton polygons with a single compact edge, we obtain an integrability criterion under appropriate conditions on the singularities of the resolved foliation.
Finally, following the classical Newton-theoretic approach to plane curves, we explore how the geometry of Newton polygons provides information about the local topology of holomorphic first integrals.