王知远博士系列学术报告
Title: Abstract QFTs and Their Realizations
Speaker: Zhiyuan Wang(王知远)
Affiliation: Peking Universtiy
Time: 14:00-15:30, Tuesday, December 21st, 2021
14:00-15:30, Wednesday, December 22nd, 2021
14:00-15:30, Thursday, December 23rd, 2021(UTC+8, Beijing Time)
Venue: Room 1502, Shing-Tung Yau Center, Yifu Architecture Building, Sipailou Campus of Southeast University, Nanjing
Inviter: Jun Wang（王俊），Yunfeng Jiang（江云峰）
Abstract
The aim of these three lectures is to introduce a formalism called abstract quantum field theories and their realizations.
The first two lectures will be pedagogical, in which I will recall some preliminaries of moduli spaces of curves, formal Gaussian integrals, integration over Hermitian matrices, and their relation to Feynman graphs. These results are well-known in literatures.
In the third lecture I will introduce the construction of the abstract QFT for stable graphs and fat graphs, and their realizations. This is a joint work with J. Zhou. We define the abstract partition function and abstract free energy as formal summations of graphs, and derive recursion relations for them using operators inspired by geometry of moduli spaces of curves. By assigning Feynman rules, we obtain some specific theories or problems and their recursion relations (such as the holomorphic anomaly type equations, Virasoro constraints, etc.) in this way.
About the Speaker
王知远，2019年博士毕业于清华大学数学科学系，导师为周坚教授。现为北京大学数学科学学院博士后，合作导师为范辉军教授。研究方向为数学物理，主要关心与量子场论和弦论有关的数学，例如镜像对称，可积系统，以及相关的组合问题等。
Slides--Wang Zhiyuan-Abstract QFTs Realizations and Recursion Relations -20211223.pdf