2022-10-04

Geometric flows, G2-structures and 3-Sasakian geometry

BIMSA-BIT Differential Geometry Seminar

报告人 Jason Lotay Oxford University

时 间 09:15-10:15 Tue

地 点 Online Zoom 559 700 6085（PW: BIMSA）

摘要

3-Sasakian 7-manifolds admit two natural Einstein metrics with positive scalar curvature, both of which are induced by special structures in 7 dimensions known as nearly parallel G2-structures. Up to scaling, Einstein metrics are critical points for the Ricci flow and nearly parallel G2-structures are critical points for two different flows in G2 geometry: the Laplacian flow and the Laplacian coflow. In this talk, I will describe how the behaviour is very different for each of these flows on 3-Sasakian 7-manifolds, particularly in terms of the stability and instability of the critical points. This is joint work with A. Kennon.

组织者：Kotaro Kawai, Sebastian Heller, Lynn Heller, Chao Qian

2022-10-04

Topological Wick rotation and holographic duality II

Category and Topological Order Seminar

报告人 孔良 南方科技大学

时 间 09:30-11:00 Tue

地 点 1131

Tencent 607 3645 0351

摘要

I will explain a new type of holographic dualities between n+1D topological orders with a chosen boundary condition and nD (potentially gapless) quantum liquids. It is based on the idea of topological Wick rotation, a notion which was first used in arXiv:1705.01087 and was named, emphasized and generalized later in arXiv:1905.04924. Examples of these holographic dualities include the duality between 2+1D toric code model and 1+1D Ising chain and its finite-group generalizations (independently discovered by many others); those between 2+1D topological orders and 1+1D rational conformal field theories; and those between n+1D finite gauge theories with a gapped boundary and nD gapped quantum liquids. I will also briefly discuss some generalizations of this holographic duality and its relation to AdS/CFT duality.

组织者：郑浩

2022-10-04

Convergence Analysis of the Uniform Framework of the Yau-Yau Algorithm

Seminar on Control theory and Nonlinear Filtering

报告人 孙泽钜 清华大学数学科学系 博士生

时 间 15:00-15:30 Tue

地 点 Online Tencent 735 7908 4302

摘要

In this talk, I will continue to discuss on the mathematical interpretation of the uniform framework of the Yau-Yau algorithm. An attempt will be made for a convergence analysis without the effect of curse of dimensionality. A desired result of this discussion will be that the number of the computation nodes will only increase polynomially, rather than exponentially, with respect to the dimension.

组织者：丘成栋

2022-10-04

Matching Normalizing Flows and Probability Paths on Manifolds

Seminar on Control theory and Nonlinear Filtering

报告人 康家熠 清华大学数学科学系 博士生

时 间 15:30-16:00 Tue

地 点 Online

Tencent 735 7908 4302

摘要

In this report, I will introduce some results on normalising flows. Continuous Normalizing Flows (CNFs) are a class of generative models that transform a prior distribution to a model distribution by solving an ordinary differential equation (ODE).

组织者：丘成栋

2022-10-07

一般量子态生成和量子电路优化的复杂性刻画

YMSC-BIMSA Quantum Information Seminar in 2022 Spring

报告人 张胜誉 腾讯量子实验室

时 间 09:30-10:30 Fri

地 点 JCY-1

Zoom 559 700 6085（PW: BIMSA）

摘要

量子算法在通用数字量子计算机上的实现一般是通过标准量子电路。随着越来越多的量子比特集成，我们在不远的将来面临大量寿命有限的量子比特。如何利用这些量子比特完成尽可能多的量子电路是一个基本的问题。在这个报告中，我们汇报最近在一般量子态生成和量子电路的优化，在任意给定数量的辅助量子比特下，给出最优的量子电路。

组织者：刘正伟