应我校数学科学学院邀请，俄罗斯新西伯利亚国立大学Nikolay Abrosimov教授将于2025年4月12日为我校师生讲学。欢迎全校相关教师、博士生、硕士生参加!

报告题目：Euclidean volume of a cone manifold over any hyperbolic knot is an algebraic number.

报告人：Nikolay Abrosimov

报告人单位：新西伯利亚国立大学

时间：2025年4月12日（周六）10：00

报告地点：数学科学学院7楼报告厅

主办单位：重点建设与发展工作处、数学科学学院

简介：Nikolay AbrosimovisDeputy director for science at Sobolev Institute of MathematicsAssociate professor and Deputy head of Chair of function theory at Novosibirsk State University,Senior researcher at Regional Mathematical Center of Tomsk State University- Visiting lecturer at Chinese-Russian Institute of Heilongjiang University (China). His research interests include geometry and topology of 3-manifolds, orbifolds, knots, and links.His main subject is obtaining exact formulas for the volume of polyhedra, 3-manifolds, and orbifolds in spaces of constant curvature. he is also interested in finding non-Euclidean versions of classical theorems from Euclidean geometry.

报告摘要：A hyperbolic structure on a three-dimensional cone manifold with a knot as a singular set can usually be deformed into a limit Euclidean structure. In our paper [1] we show that thecorresponding normalized Euclidean volume of the manifold is always an algebraic number i.e.a root of some polynomial with integer coefficients. This result is a generalization (for cone manifolds) of the well-known Sabitov theorem on the volumes of Euclidean polyhedra which gave an answer to the bellows problem. The fact we established stands out against the backgroundof hyperbolic volumes the number-theoretic nature of which is usually quite complex. In addition to this theorem we propose an algorithm that allows one to explicitly calculate the minimal polynomial for a normalized Euclidean volume.

欢迎各位老师同学届时参加！