主持人：刘博 教授

报告摘要：
Homologically area-minimizing subvarieties arise throughout geometry, for example as holomorphic subvarieties in K?hler manifolds and as special Lagrangians in Calabi–Yau manifolds. Classical intuition, reinforced by nearly all known examples, suggests that such minimizers should be subanalytic, generically smooth, and calibrated. We show that this picture is fundamentally false. We prove that all of these expected properties fail generically. In particular, we construct homologically area-minimizing subvarieties with fractal singular sets. Moreover, we show that smoothable singularities and calibrated minimizers are non-generic phenomena. Consequently, we resolve several longstanding conjecture of Almgren, Morgan and White. To organize this unexpectedly rich behavior, we establish that the number-theoretic Hasse principle holds for area-minimizing subvarieties, providing a new framework that links geometric analysis, topology, and number theory.

报告人简介：
刘臻化中学毕业于华东师范大学第二附属中学，本科毕业于杜克大学，即将普林斯顿大学博士毕业。独立作者论文见于Annals of Mathematics， Duke Mathematical Journal，Communications on Pure and Applied Mathematics。