2022-11-07

A Geometric Model for the Module Category of a Skew-gentle Algebra

BIMSA Topology Seminar

报告人 何平 BIMSA

时 间 15:30-17:00 Mon

地 点 1129B

Zoom 537 192 5549（PW: BIMSA）

摘要

The main object of this report is to give a geometric model for the module category of a skew-gentle algebra via a partial ideal/tagged triangulation on a puncture marked surface. On the one hand, by using this model, we give a geometrical realization of a class of indecomposable modules and the Auslander-Reiten translations; we also give an intersection-dimension formula which shows that the dimension of a morphism space equals to the intersection number of corresponding curves. In particular, support τ -tilting modules can be classified. On the other hand, we study the two-term rigid subcategory of a (2-Calabi-Yau) triangulated categories and show that it admits cluster structures. Such a clsuter structure can be geometricall interpreted after we generalizing our model to the so called surface rigid algebra. We give a combinatorial proof to show that the cluster structure is mutation-connected, which implies the support τ -tilting graph of a skew-gentle algebra is connected. Finally, by constructing morphisms explicitly, we also give the fundamental group of the support τ -tilting graph over a gentle algebra.

组织者：吴杰, 杨南君, 李京艳

2022-11-08

Equidistribution in Stochastic Dynamical Systems

BIMSA-YMSC Tsinghua Number Theory Seminar

报告人 Bella Tobin Oregon State University

时 间 10:30-11:30 Tue

地 点 1118

Zoom 293 812 9202（PW: BIMSA）

摘要

In arithmetic dynamics, one typically studies the behavior and arithmetic properties of a rational map under iteration. Instead of iterating a single rational map, we will consider a countable family of rational maps, iterated according to some probability measure. We call such a system a stochastic dynamical system. As such a family can be infinite and may not be defined over a single number field, we introduce the concept of a generalized adelic measure, generalizing previous notions introduced by Favre and Rivera-Letelier and Mavraki and Ye. Generalized adelic measures are defined over the measure space of places of an algebraic closure of the rational numbers using the framework established by Allcock and Vaaler. This turns heights from sums into integrals. We prove an equidistribution result for generalized adelic measures, and in turn prove an equidistribution theorem for random backwards orbits for stochastic dynamical systems. This talk will include some background in arithmetic dynamics and will be suitable for graduate students.

组织者：Hansheng Diao, Yueke Hu, Emmanuel Lecouturier, Cezar Lupu

2022-11-08

A minimalist's approach to the physics of emergence

Category and Topological Order Seminar

报告人 邹柳俊 Perimeter Institute

时 间 21:00-22:30 Tue

地 点 1131

Zoom 537 192 5549（PW: BIMSA）

摘要

One of the central themes of quantum many-body physics and quantum field theory is the emergence of universality classes. In general, it is highly complex to determine which universality class emerges in a quantum many-body system based on its microscopic properties. In this talk, I will argue that the perspective of quantum anomaly provides powerful insights into the understanding of the landscape of universality classes that can emerge in a quantum matter, and I will present some interesting applications. Along the way, we will discuss the notion of entanglement-enabled symmetry-breaking orders, non-Lagrangian quantum criticality, quantum spin liquids beyond the usual parton description, etc.

组织者：郑浩

2022-11-10

Data driven method to learn the stochastic dynamical systems and its application in polymer dynamics

BIMSA-Tsinghua Seminar on Machine Learning and Differential Equations

报告人 陈小丽 新加坡国立大学

时 间 09:00-10:30 Thu

地 点 1129B

Zoom 537 192 5549（PW: BIMSA）

摘要

In this talk, I will discuss how to use machine learning method to learn the stochastic problem. To begin, I will introduce the how to combine physics informed neural network(PINN) method and the sample observation data to learn the stochastic differential equation driven by Brown and Levy noise. Second, I will introduce how to use stochatic OnsagerNet to learn closure dynamical systems. We propose a general machine learning approach to construct reduced models for noisy, dissipative dynamics based on the Onsager principle for non-equilibrium systems. Then I will demonstrate our method by modelling the folding and unfolding of a long polymer chain in an external field - a classical problem in polymer rheology - though our model is suitable for the description of a wide array of complex, dissipative dynamical systems arising in scientific and technological applications.

人物介绍

陈小丽，2020年博士毕业于华中科技大学。2018年9月至2020年8月在美国布朗大学进行联合培养。2021年3月至今在新加坡国立大学数学系和功能智能材料研究院(I-FIM)做博士后研究。主要从事随机动力系统, 机器学习与动力系统的研究。已在SIAM Journal on Scientific Computing, Physica D, Chaos等期刊发表多篇学术论文。

组织者：熊繁升, 杨武岳, 雍稳安, 朱毅

2022-11-10

Optimal control and nonlinear filtering

Internal Seminar on Machine Learning and Differential Equations

报告人 焦小沛 BIMSA

时 间 14:00-16:00 Thu

地 点 1129B

组织者：熊繁升, 杨武岳

2022-11-11

Square root of modular tensor category

YMSC-BIMSA Quantum Information Seminar

报告人 郑浩 BIMSA, YMSC

时 间 09:30-10:30 Fri

地 点 清华大学近春园西楼一层报告厅

Tencent 337 8937 1456

摘要

The problem of solving square root of a modular tensor category is motivated by 3D extended topological field theories and gapless edges of 3D topological orders. We supply a solution to this problem by using enriched fusion categories.

组织者：刘正伟

2022-11-12

Recent advance in breathers of Manakov equations

Integrable Systems Seminar

报告人 刘冲 西北大学物理学院

时 间 09:00-10:30 Sat

地 点 Online

Tencent 461 747 037

摘要

Manakov equations play a key role in understanding nonlinear coupling in many physical contents with different scales in time and space, including optics, cold atoms, crossing seas, and even financial systems. Finding new nonlinear wave phenomena and understanding their physics in Manakov equations are still a challenge in both physics and mathematics. We will present in this talk our recent results for a particular type of oscillating localised structures (known as “breathers”) of Manakov equations. These include non-degenerate breathers and their role in vector modulation instability.

人物介绍

刘冲，西北大学理论物理团队成员，副教授，入选陕西省“特支”计划、陕西省青年科技新星。主要关注非线性物理的不稳定性理论。以第一/通讯作者在具有重要影响力的学术刊物（Phys.Rev.Lett.,Phys.Rev.E 等）上发表论文三十余篇，撰写专著《可积模型方法及其应用》第四章。

组织者：王丽, 张国强