学术报告

报告题目：TBA equations and Schrödinger equation with angular momentum

报 告  人：束红非 (Hongfei Shu)

报告时间：2019-05-14上午10点

报告地点： 理6-301

报告摘要：

The ODE/IM correspondence describes the relation between the spectral analysis of ordinary differential equations (ODE) and the functional relations approach of the two-dimensional quantum integrable models (IM). In this talk, we focus on the Schrödinger equation of one-dimensional Quantum Mechanics, which is a typical example of the second order ODE. We derive a system of Thermodynamic Bethe ansatz (TBA) equations governing the exact WKB periods in one-dimensional Quantum Mechanics with arbitrary polynomial potentials and angular momentum. These equations provide a generalization of the ODE/IM correspondence, and can be regarded as the solution of a Riemann-Hilbert problem in resurgent Quantum Mechanics formulated by Voros. We also show that our TBA equations, combined with exact quantization conditions, provide a powerful method to solve spectral problems in Quantum Mechanics. We illustrate our general analysis with a detailed study of cubic oscillators. This talk is based on the work with Katsushi Ito and Marcos Marino [arXiv: 1811.04812] and work in progress.

个人简介

Dr. Hongfei Shu obtained his B.S. at Tokyo Institute of Technology in Japan in 2014, MS in Tokyo Institute of Technology (Prof. Katsushi Ito’s group, Japan) in 2016, and completed his Ph.D. in Tokyo Institute of Technology (Prof. Katsushi Ito’s group, Japan) in 2019. He will move to Nordita Sweden in this fall as postdoc. He received JSPS Research Fellowship for Young Scientists from 2017 to 2019. Currently, he is a special PD researcher in Tokyo Institute of Technology. His research interest includes Integrability, N=2 Gauge theory and AdS/CFT correspondence.

报告题目：超对称代数、全息核物质理论与引力波事件

报告人：张弘   国立台湾师范大学

时间：2019年5月14日  下午14：00

地点：大学城校区理六栋301

邀请人：马承德

报告摘要：

第一部分：Alday-Gaiotto-Tachikawa (AGT)猜想中隐含的共形对称性由W代数描述，与仿射Yangian同构，也是高自旋/CFT对偶的核心。通过增加一个参数会得到Ding-Iohara-Miki代数，我们将讨论它们的水平表象、垂直表象及qq指标。而N=2超对称版本的仿射Yangian则可利用顶点运算代数的理念，通过用无限长管道连接两个平面配分表象得到。

    第二部分：我们利用量子色动力学力学的全息模型，导出了有适中重子密度的低温核物质的状态方程。这利用了在非禁闭Witten几何的Sakai-Sugimoto模型，以额外的点近似D4-膜瞬子构造作为全息重子。我们得到的状态方程为双-多回归形式，其声速满足因果律限制并且突破音障。将它代入Tolman-Oppenheimer-Volkoff方程组后可以得到致密星体的质量，致密度与潮汐形变，与LIGO/Virgo的引力波观测中子星合并事件GW170817的数据分析结果一致。

报告人简介：

张弘，2004-2008，清华大学工程物理系工学学士，毕业论文题目为“引力波与多极矩分析”，探讨利用低成本的金属量子跃迁来探测引力波的可能性。2008-2013，日本东京大学物理系理学硕士、博士， 博士论文题目为“Selberg积分与规范/Toda对偶”，研究超弦理论与数学物理学，致力于AGT猜想的证明与推广。2013-2014，日本中央大学博士后，研究超弦理论与数学物理学。2014-2016，韩国西江大学博士后，研究 W代数与Ding-Iohara-Miki代数。2016-2018，中科院理论物理研究所博士后，研究超对称仿射Yangian。2018年至今，台湾师范大学博士后，研究数学物理学、超弦理论与引力波观测。