The translation geometry of Polya's shires
演讲者
时间
2026年04月16日 15:00 至 16:00
地点
A6-101
线上
Zoom 442 374 5045
(BIMSA)
摘要
In his shire theorem, Polya proves that the zeros of iterated derivatives of a rational function in the complex plane accumulate on the union of edges of the Voronoi diagram of the poles of this function. Recasting the local arguments of Polya into the language of translation surfaces, we prove a generalization describing the asymptotic distribution of the zeros of a meromorphic function on a compact Riemann surface under the iterations of a linear differential operator defined by meromorphic 1-form. The accumulation set of these zeros is the union of edges of a generalized Voronoi diagram defined jointly by the initial function and the singular flat metric on the Riemann surface induced by the differential. This process offers a completely novel approach to the practical problem of finding a flat geometric presentation (a polygon with identification of pairs of edges) of a translation surface defined in terms of algebraic or complex-analytic data. In the first part of the talk, we will give background on translation surfaces and their links with dynamical systems.
This is a joint work with Rikard Bogvad, Boris Shapiro and Sangsan Warakkagun.
This is a joint work with Rikard Bogvad, Boris Shapiro and Sangsan Warakkagun.
演讲者介绍
Tahar是BIMSA助理研究员。在加入BIMSA之前，他曾在魏茨曼科学研究所担任高级博士后研究员。他致力于平面上各种几何结构的模空间研究，包括平移和扩张结构、平坦度规和锥球度规。Guillaume-Tahar最近的研究兴趣涉及线性微分算子、isoresidual fibrations和simplicial arrangements of lines.