2022-11-14 Mon
Application of multi-commodity flows to holographic quantum entanglement
BIMSA Topology SeminarSpeaker: Yiyu Lin BIMSA
Time: 15:30-17:00
Venue: Online
Zoom: 537 192 5549（PW: BIMSA）
Abstract
Many concepts from quantum information theory and network theory have proved useful in the study of holographic duality or emergent gravity. This talk will focus on a simple application of the concepts of conditional mutual information (CMI) from quantum information theory and multi-commodity flow (multiflow) from network theory in this regard. In fact, the embodiment of this application is the bit-thread formulation of the Ryu-Takayanagi formula of holographic entanglement entropy. This talk aims to present a "thread" perspective, which is complementary to the "local tensor" perspective in the holographic tensor network models, to investigate the structure of quantum entanglement in holographic duality.
Organizers：Jie Wu, Nanjun Yang, Jingyan Li
2022-11-15 Tue
A new proof of Gromov's almost flat manifolds theorem
BIMSA-BIT Differential Geometry SeminarSpeaker: Xiaochun Rong Rutgers University
Time: 09:15-10:15
Venue: Online
Zoom: 559 700 6085（PW: BIMSA）
Abstract
We will discuss a new proof for the Gromov's theorem on almost flat manifolds, which is an inductive proof on dimension.
Organizers：Kotaro Kawai, Sebastian Heller, Lynn Heller, Chao Qian
2022-11-15 Tue
Minimal extensions of symmetric fusion categories and Witt groups
Category and Topological Order SeminarSpeaker: Dmitri Nikshych University of New Hampshire
Time: 13:30-15:00
Venue: 1131
Zoom: 559 700 6085（PW: BIMSA）
Abstract
Groups of minimal extensions of symmetric fusion categories were introduced by Lan, Kong, and Wen to study symmetry protected topological phases of matter. We describe how these groups are related to categorical Witt groups and how to compute them using a categorical analogue of the Kunneth formula in group cohomology.
Organizers：Hao Zheng
2022-11-15 Tue
Quantitative weak approximation of rational points on quadrics
BIMSA-YMSC Tsinghua Number Theory SeminarSpeaker: Zhizhong Huang AMSS, CAS
Time: 16:00-17:00
Venue: Ning Zhai W11
Zoom: 293 812 9202（PW: BIMSA）
Abstract
The classical Hasse—Minkowski theorem states that rational points on quadrics (if non-empty) satisfy weak approximation. We explain how Heath-Brown’s delta circle method allows to obtain a quantitive and effective version of this theorem, namely counting rational points of bounded height on quadrics satisfying prescribed local conditions with optimal error terms. We then discuss applications in intrinsic Diophantine approximation on quadrics. This is based on joint work in progress with M. Kaesberg, D. Schindler, A. Shut.
Organizers：Hansheng Diao, Yueke Hu, Emmanuel Lecouturier, Cezar Lupu
2022-11-16 Wed
Orbifold theory and modular extensions
BIMSA-Tsinghua Quantum Symmetry SeminarSpeaker: Chongying Dong University of California at Santa Cruz
Time: 10:30-12:00
Venue: 1131
Zoom: 537 192 5549（PW: BIMSA）
Abstract
Orbifold theory studies a vertex operator algebra V under the action of a finite automorphism group G. The main objective is to understand the module category of fixed point vertex operator subalgebra V^G. This talk will explain how to use the results on modular extensions by Drinfeld-Gelaki-Nikshych-Ostrik and Lan-Kong-Wen to study the module category of V^G. If V is holomorphic then the V^G-module category is braided equivalent to the module category of some twisted Drinfeld double associated to a 3-cocycle in H^3(G,U(1)). This result has been conjectured by Dijkgraaf-Pasquier-Roche. This is a joint work with Richard Ng and Li Ren.
Organizers：Zhengwei Liu, Sebastien Palcoux, Yilong Wang, Jinsong Wu
2022-11-17 Thu
Symmetry-preserving machine learning for computer vision, scientific computing, and distribution learning
BIMSA-Tsinghua Seminar on Machine Learning and Differential EquationsSpeaker: Wei Zhu University of Massachusetts Amherst
Time: 10:00-11:30
Venue: 1129B
Zoom: 537 192 5549（PW: BIMSA）
Abstract
Symmetry is ubiquitous in machine learning and scientific computing. Robust incorporation of symmetry prior into the learning process has shown to achieve significant model improvement for various learning tasks, especially in the small data regime. In the first part of the talk, I will explain a principled framework of deformation-robust symmetry-preserving machine learning. The key idea is the spectral regularization of the (group) convolutional filters, which ensures that symmetry is robustly preserved in the model even if the symmetry transformation is “contaminated” by nuisance data deformation. In the second part of the talk, I will demonstrate how to incorporate additional structural information (such as group symmetry) into generative adversarial networks (GANs) for data-efficient distribution learning. This is accomplished by developing new variational representations for divergences between probability measures with embedded structures. We study, both theoretically and empirically, the effect of structural priors in the two GAN players. The resulting structure-preserving GAN is able to achieve significantly improved sample fidelity and diversity—almost an order of magnitude measured in Fréchet Inception Distance—especially in the limited data regime.
Speaker Intro
Wei Zhu is an Assistant Professor at the Department of Mathematics and Statistics, University of Massachusetts Amherst. He received his B.S. in Mathematics from Tsinghua University in 2012, and Ph.D. in Applied Math from UCLA in 2017. Before joining UMass, he worked as a Research Assistant Professor at Duke University from 2017 to 2020. Wei is interested in developing theories and algorithms in statistical learning and applied harmonic analysis to solve problems in machine learning, inverse problems, and scientific computing. His recent research is particularly focused on exploiting and discovering the intrinsic structure and symmetry within the data to improve the interpretability, stability, reliability, and data-efficiency of deep learning models.
Organizers：Fansheng Xiong, Wuyue Yang, Wen-An Yong, Yi Zhu
2022-11-18 Fri
量子计算机的建造难点—如何实现抗噪
YMSC-BIMSA Quantum Information Seminar in 2022 SpringSpeaker: Dong Liu Tsinghua University, Beijing Academy of Quantum information Sciences
Time: 09:30-10:30
Venue: JCY-1
Tencent: 337 8937 1456
Abstract
量子计算机能否被建造出来，如果原理上可以的话它的建造难度是什么？这个问题背后的核心是：量子系统如何抗噪。为了实现量子计算的抗噪，我们一般从几个方面来考虑：1）量子硬件的制备和实验提升，2）量子系统的控制方法，3）容错性量子计算的算法软件的构建。本报告将会对后面两个问题进行阐述，并且试图从理论层面提出新的科学问题。 首先我们讨论一下量子计算机的核心控制部分—校准系统。当量子芯片的比特数目变大并且量子运算更加复杂时，各个比特之间不可避免的有相互影响，导致操控变得复杂。同时受环境和器件影响，比特的参数会随时间漂移从而影响操控和测量，导致量子计算出现严重错误。因此，如何实现量子芯片的自动控制和实时维护是实现量子计算的核心。我们将重点讨论并且提出量子计算机校准控制中的科学问题。 其次，量子纠错编码是实现通用容错量子计算的一个重要方案。我们发现表面码在测量诱导的相干错误下会产生不能被探测到的错误，这些错误将累积并演变为逻辑错误。这种现实上可能出现的重要错误会使量子码变成“近似”量子纠错码，这种效应会使量子纠错程序在更多次循环后变得非常有害。考虑到容错量子计算的实现复杂度和理论上的问题。但是，我们的结果表明：通过增加量子编码的尺度可以显著的减小这种危害性。近期量子计算中需要尽可能考虑复杂度较低的针对特定问题设计的抗噪量子算法。最后，我们介绍一个基于随机编译方案的抗噪量子相位估计算法的设计和原理。
Speaker Intro
刘东副教授于2018年5月加入清华大学物理系，在2020年加入北京量子信息研究院成为兼任研究员，并且负责“量子操作系统”团队。他分别于2005、2012年在北京大学和杜克大学获得学士和博士学位，之后在密西根州立大学和微软研究院Station Q从事博士后研究，并且在2018年入选某海外高层次青年人才计划。刘东课题组近五年主要致力于拓扑量子器件的验证方案、量子计算机的体系结构、非平衡多体量子物理的量子场论方法等方向的理论研究。
Organizers：Zhengwei Liu
2022-11-18 Fri
TBA
Math and Biology SeminarSpeaker: Xiaoxian Tang Beihang Uinversity
Time: 10:30-11:30
Venue: Online
Zoom: 293 812 9202（PW: BIMSA）
Organizers：Jie Wu, Jingyan Li, Xiang Liu, Fedor Pavutnitskiy
