公开课/COURSE

讨论班/SEMINAR

2022-09-26

Monodromy and period map of the Winger Pencil

BIMSA Topology Seminar

报告人 自云鹏

时 间 15:30-17:00 Mon

地 点 1129B

Zoom 537 192 5549（PW: BIMSA）

摘要

We investigate the moduli space of genus 10 curves that are endowed with a faithful action of the icosahedral group $\Acal_5$. We will show among other things that this moduli space essentially consists two copies of the pencil of plane sextics introduced by Winger, an American mathematician, in 1924 with the unique unstable member (a triple conic) replaced by a smooth non-planar curve. We also prove that the Jacobian of a smooth member of the Winger pencil contains the tensor product of an elliptic curve with a certain integral representation of the icosahedral group. We find that the elliptic curve comes with a distinguished point of order $3$, prove that the monodromy on this part of the homology is the full congruence subgroup $\Gamma_1(3)\subset \SL_2(\Zds)$ and subsequently identify the base of the pencil with the associated modular curve. Except those we also observed that the Winger pencil `accounts' for the deformation of the Jacobian of Bring's curve as a principal abelian fourfold with an action of the icosahedral group.

组织者：吴杰, 杨南君, 李京艳

2022-09-27

The plectic conjecture over local fields

BIMSA-YMSC Tsinghua Number Theory Seminar

报告人 Siyan Daniel Li-Huerta Harvard University

时 间 10:00-11:00 Tue

地 点 1118

Zoom 293 812 9202（PW: BIMSA）

摘要

The étale cohomology of varieties over Q enjoys a Galois action. For Hilbert modular varieties, Nekovář-Scholl observed that this Galois action on the level of cohomology extends to a much larger profinite group: the plectic group. Motivated by applications to higher-rank Euler systems, they conjectured that this extension holds even on the level of complexes, as well as for more general Shimura varieties. We present a proof of the analog of this conjecture for local Shimura varieties. Consequently, we obtain results for the basic locus of global Shimura varieties, after restricting to a decomposition group. The proof crucially uses a mixed-characteristic version of fusion due to Fargues–Scholze.

组织者：Cezar Lupu

2022-09-27

Topological Wick rotation and holographic duality

Category and Topological Order Seminar

报告人 孔良 南方科技大学

时 间 13:30-15:00 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. I will provide some explicit examples in low dimensions, including the duality between 2+1D toric code model and 1+1D Ising chain and its finite-group generalizations (independently obtained by Freed and Teleman arXiv:1806.00008); that between 2+1D topological orders and 1+1D rational conformal field theories. As a consequence, we immediately obtain the classification of all 1+1D gapped quantum phases, a result which was obtained previously via a very different approach. This classification result generalizes to gapped quantum liquids in higher dimensions (with more general symmetries). I will also discuss some generalizations of this holographic duality and its relation to AdS/CFT duality.

组织者：郑浩

2022-09-29

Multiple soliton of the nonlinear Schrodinger equation and its regularity

Integrable Systems Seminar

报告人 张永帅 浙江科技学院

时 间 09:00-10:00 Thu

Tencent 713 979 838

摘要

In this talk, we consider the Riemann-Hilbert approach of the nonlinear Schrodinger (NLS) equation. By constructing and solving the Riemann-Hilbert problem with multiple high-order poles, we get the multiple soliton solution of NLS equation. By decomposing the matrix, we prove the regularity of this type soliton.

组织者：王丽, 张国强

2022-09-29

基于深度学习的分子动力学模拟

BIMSA-Tsinghua Seminar on Machine Learning and Differential Equations

报告人 王涵 北京应用物理与计算数学研究所

时 间 10:00-11:30 Thu

地 点 1129B

Zoom 537 192 5549（PW: BIMSA）

摘要

分子动力学模拟需要对原子间相互作用（势函数）有一个精确的描述，然而人们面临两难困境：第一性原理方法精确但昂贵，经验势方法快速但精度有限。我们在报告中从两个方面讨论了解决办法：势函数构造和数据生成。在势函数构造方面，我们介绍深度势能方法及其最新进展，包括更强大的描述子和长程相互作用建模。在数据生成方面，我们介绍同步学习格式DP-GEN：通过探索构型和化学空间持续改进深度势能。在报告的最后部分，我们介绍深度势能方法在水相图计算上的应用。

人物介绍

王涵，北京应用物理与计算数学研究所特聘研究员，博士生导师。2011年毕业于北京大学数学科学学院，获得理学博士学位；2011至2014年于柏林自由大学数学与计算机学院从事博士后研究。2014年加入北京应用物理与计算数学研究所，任助理研究员，副研究员，特聘研究员。主要研究兴趣为分子动力学模拟中的多尺度建模与计算方法。与合作者发展了基于深度学习的原子间相互作用建模与计算方法，解决了传统方法精度和效率无法两全的困境，将第一原理精度分子动力学模拟规模推进至亿原子量级。

组织者：熊繁升, 杨武岳, 雍稳安, 朱毅

2022-09-29

Leibenson's equation on Riemannian manifolds

AMSS-YMSC-BIMSA Joint Seminar on Progress of Topology and Its Applications

报告人 Alexander Grigoryan Universität Bielefeld

时 间 17:00-18:30 Thu

地 点 1120

Zoom 518 868 7656（PW: BIMSA）

摘要

We consider on arbitrary Riemannian manifolds the Leibenson equation: $$\partial _{t}u=\Delta _{p}u^{q}.$$ This equation comes from hydrodynamics where it describes filtration of a turbulent compressible liquid in porous medium. Here $u(x,t)$ is the fraction of the volume that the liquid takes in porous medium at time $t$ at point $x$. The parameter $p$ characterizes the turbulence of a flow, while $q$ describes the compressibility of the liquid. We prove that if $p>2$ and $1/(p-1)<q\leq 1$="" then="" solutions="" of="" this="" equation="" have="" finite="" propagation="" speed.="" on="" complete="" manifolds="" with="" non-negative="" ricci="" curvature,="" we="" obtain="" a="" sharp="" rate="" that="" matches="" barenblatt="" solution.

人物介绍

Professor Alexander Grigor'yan received his PhD from Lomonosov Moscow University in 1982. Since then, he worked at the State University of Volgograd and the Institute of Control Sciences in Moscow with receiving his habilitation in 1989. He has been a Humboldt Fellow at Bielefeld University in 1992-93 and a Guest Scholar at Harvard University in 1993/94. After working from lecturer to professor at Imperial College London in 1994-2005, he became a professor at Bielefeld University from 2005. Professor Grigor'yan won a gold medal at International Mathematical Olympiad when he was 17, awarded by the Prize of the Moscow Mathematical Society in 1988, and received the Whitehead Prize of London Mathematical Society in 1997. He was an invited speaker of European Congress of Mathematicians in Barcelona in 2000. Professor Grigor'yan is one of the top experts in geometric analysis on Riemannian manifolds, metric spaces and graphs, with making various important contributions on the topics.

组织者：吴杰

2022-09-30

量子电路优化中的一个数学问题

YMSC-BIMSA Quantum Information Seminar in 2022 Spring

报告人 孙晓明 Institute of Computing Technology, CAS

时 间 09:30-12:15 Fri

地 点 JCY-1

Zoom 559 700 6085（PW: BIMSA）

摘要

量子线路是描述量子算法的通用数学模型和具体实现方案，当前量子计算的研发已经进入含噪声中等尺度量子系统（NISQ）阶段，对量子线路的优化是当前NISQ阶段量子计算研究的一个热点。在这一报告中我们将汇报最近在CNOT量子电路优化方面的一些工作进展，并介绍我们由此抽象出来的一个一般化的数学问题，以及其与shuffle-exchange问题的潜在联系。

人物介绍

孙晓明，中科院计算所研究员，量子计算实验室主任。主要研究领域为算法与复杂性、量子计算等。曾获首批优青、首批万人计划青年拔尖人才资助，目前担任CCF理论专委会主任。

组织者：刘正伟