Minimal Surfaces and
Alternating Multiple Zetas
报告专家：杨琳 研究员（北京雁栖湖应用数学研究院）
报告时间：2025年4月28日（星期一)下午4:00-5:00
报告地点：国家天元数学西南中心516
报告摘要：In this talk we show for every sufficiently large integer g the existence of a complete family of closed and embedded constant mean curvature (CMC) surfaces deforming the Lawson surfaces ξ1,g parametrized by their conformal type. When specializing to the minimal case, we discover a pattern resulting in the coefficients of the involved expansions being alternating multiple zeta values (MZVs), which generalizes the notion of Riemann's zeta values to multiple integer variables. This allows us to extend a new existence proof of the Lawson surfaces ξ1,g to all g≥3 using complex analytic methods and to give closed form expressions of their area expansion up to order 7. For example, the third order coefficient is 9/4ζ(3). As a corollary, we obtain that the area of ξ1,g is monotonically increasing in their genus g for all g≥0. This is joint work with Steven Charlton, Sebastian Heller, and Martin Traizet.
专家简介：杨琳研究员（北京雁栖湖应用数学研究院）于2003-2008年在柏林工业大学学习经济学和在柏林工业大学学习数学，并于2012年在图宾根埃伯哈德卡尔斯大学获得博士学位。此后，她留在图宾根做博士后，直到2017年在汉诺威莱布尼茨大学获得初级教授职位。其在微分几何上有近10年的研究科研经历，特别是三维情况下的 constantmean-curvature (CMC)曲面和 constrained Willmore 曲面的微分几何问题，涵盖几何分析，可积系统，李代数，代数几何等多个领域。在国际重要期刊上发表论文20余篇，引用100余次，H指数6。在国际会议上受邀参与报告20余次。
邀请人：Rodsphon Rudy
