讲座题目：EUCLIDIAN VOLUME OF A CONE MANIFOLD OVER ANY HYPERBOLIC KNOTIS AN ALGEBRAIC NUMBER

主办单位：三峡数学研究中心/理学院

报告专家：Nikolay Abrosimov

报告时间：2024年4月11日（星期四）14：30

报告地点：三峡数学研究中心L1218

专家简介：Nikolay Abrosimov现任Sobolev数学研究所的高级研究员，研究三维流形、轨形、结和链的几何与拓扑学。主要课题是在恒定曲率的空间中获得多面体、三维流形和轨形的体积的准确公式。并且寻找欧几里得几何学经典定理的非欧几里得版本感兴趣。

报告摘要：The talk is based on our joint work with Alexander Kolpakov (Université de Neuchâtel,Switzerland) and Alexander Mednykh (Sobolev Institute of Mathematics, Russia).The hyperbolic structure on a 3-dimensional cone-manifold with a knot as singularity canoften be deformed into a limiting Euclidean structure. In our work we show that therespective normalized Euclidean volume is always an algebraic number, that is the rootof some polynomial with integer coefficients. This result serves as a generalization (forcone manifolds) of the celebrated theorem by Sabitov on the volumes of Euclideanpolyhedra, which settles the Bellows Conjecture. The fact we have established standsout against the background of hyperbolic volumes, the number-theoretic nature of whichis usually very complex. In addition to this result, we propose an algorithm that allows oneto explicitly calculate the minimum polynomial for the normalized Euclidean volume.