Non-simply connected Calabi–Yau threefolds are important in string compactifications and are often constructed as free quotients of simply connected manifolds by discrete symmetries. For complete intersection Calabi–Yau threefolds (CICYs), previous classifications focused on symmetries induced by linear actions on ambient projective spaces, which can depend on the chosen description of the manifold. In this talk, I present a systematic classification of cyclic symmetries acting freely on CICY threefolds using recently developed favorable descriptions and character-valued index techniques, leading to the discovery of genuinely new free quotients. I will also discuss recent progress in applying machine learning methods to identify free quotients of CICYs, highlighting their potential for efficiently advancing the classification of non-simply connected Calabi–Yau manifolds.

王军涛，河北邯郸大名县人，2021年博士毕业于美国弗吉尼亚理工大学，2021年至今在北京雁栖湖应用数学研究院先后任职博士后及助理教授。研究方向为与弦论紧化相关的数学及物理，包括卡拉比-丘流形的分类和数学性质、杂化弦中粒子物理模型的构建以及如何利用机器学习方法进行相关复杂数学问题计算。