报告题目：4d N = 2 SCFTs from Calabi–Yau Singularities

报告人：杨培赫 博士后（清华大学丘成桐数学中心）

报告时间：2026 年 11 月 19 日（周四）15 : 30-16 : 30

报告地点：北洋园校区 49 教 410 室

报告摘要：

Four-dimensional N=2 superconformal field theories (SCFTs) play an important role in understanding strongly coupled quantum field theories and their connections to geometry and representation theory. A large class of these theories can be engineered from Calabi–Yau threefold singularities through string theory compactifications. Understanding how the geometric structures of Calabi–Yau singularities encode the physical properties of these theories is a central theme in the study of geometric engineering.

In this talk, we first review the geometric engineering of 4d N=2 SCFTs in Type IIB string theory and explain how their Coulomb-branch data can be extracted from singularity deformations. We then discuss recent progress in determining Higgs branches using Type IIA string theory, crepant resolutions, and Gopakumar–Vafa invariants. For more complicated singularities involving compact exceptional divisors, we explore the connection to five-dimensional SCFTs and show how magnetic quivers and Hasse-diagram inversion can be used to study the corresponding four-dimensional Higgs branches. We also discuss the construction of BPS quivers from vanishing cycles and intersection pairings, together with their connections to Schur indices and VOAs. Finally, motivated by Calabi–Yau mirror symmetry, we present recent attempts to extract Coulomb-branch data directly from Type IIA geometry using jet schemes and related geometric methods, including applications to orbifold singularities.

This talk is based on our recent work arXiv:2603.01742 and several ongoing projects.

报告人简介：

杨培赫，现任清华大学丘成桐数学科学中心博士后。2018年本科毕业于中国地质大学（武汉），随后于天津大学完成硕士及博士阶段的学习。2024年至2026年在北京大学高能物理研究中心从事博士后研究，并于2026年9月起加入清华大学丘成桐数学科学中心，继续开展博士后研究工作。博士及硕士期间，主要研究方向为 AdS/CFT 对应中的可积性问题。目前主要研究兴趣包括超共形场论（SCFT）与顶点算子代数（VOA）之间的对应关系，以及具有八个超荷的超对称理论的几何工程。