星光直播 星光直播 报告[2026]045号

(高水平大学建设系列报告1304号)

报告题目：The translation geometry of Polya's shires

报告人： Guillaume Tahar 助理研究员 （北京雁栖湖应用数学研究院）

报告时间：2026年5月18日9:30-10:30

报告地点：汇文楼办公区1420

报告内容：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.

报告人简介：Guillaume Tahar obtained his Ph.D from Université Paris Diderot, under the supervision of Anton Zorich. He was a senior postdoctoral fellow at the Weizmann Institute of Science and joined BIMSA as an Assistant Professor in 2022. His research focuses on geometric structures on surfaces, with applications to moduli spaces and dynamical systems. He contributed to the study of various flavours of geometric structures, including translation surfaces, polyhedral metrics, cone spherical metrics and complex affine structures. His approach typically involves a mix of complex analysis, geometric constructions, and combinatorial reasoning. His key results include the proof of the existence of closed geodesics in dilation surfaces, the complete characterization of configurations of local invariants realized by a differential on a Riemann surface and the establishment of Grünbaum's asymptotic classification for simplicial line arrangements with few double points. His recent research interests include the topological interpretation of quantum invariants of knots, the counting of BPS states in quantum field theory and holomorphic dynamics in higher dimensions.

欢迎师生参加！

邀请人：周泽

星光直播

2026年5月11日