2024-07-29 ~ 2024-08-02
2024-06-11 ~ 2024-06-16
2024-04-29 ~ 2024-05-03
2024-04-12 ~ 2024-04-14
2024-04-08 ~ 2024-04-12
Intelligent Computing for Inverse Problems and Data Science
会议编号:
M240701
时间:
2024-07-29 ~ 2024-08-02
浏览次数:
688
SIMIS-TSIMF Interdisciplinary Series-Thermodynamics of Complexity: Free Energy Approach
会议编号:
M240601
时间:
2024-06-11 ~ 2024-06-16
浏览次数:
183
上海数学与交叉学科研究院(SIMIS)依托清华三亚数学科学论坛(TSIMF)举办“复杂系统的热⼒学:⾃由能原理”小型研讨会,邀请物理学、数学、计算神经科学、⼈⼯智能等具有交叉背景和兴趣的专家,聚焦⾮平衡态统计与复杂动⼒系统的数学刻画,探讨⾃适应体系的⾃组织与演化的第⼀性原理和复杂系统的涌现现象。研讨会将深⼊探讨⼀下课题,1)⾮平衡态统计物理;2)⾼维动⼒系统、临界性、随机过程; 3)信息论、编码理论。研讨会将⾸先回顾 Jarzynski,Crooke, Seifert 等研究的⾮平衡态热⼒学⾥熵与⾃由能的基本概念、Shannon 信息论信源信道编码和Bialek 的信息瓶颈原理、计算神经科学领域提炼出的⻉叶斯预测编码、主动推理和 Friston 的⼤脑⾃由能原理等,通过⾃由⽽聚焦的跨学科讨论,探索描绘信息运动及其随机控制的⼀般动⼒学规律和⽅程。
研讨会形式:研讨会在海南省三亚市的清华三亚国际数学论坛(TSIMF)举⾏。预计 4-5 天时间,规模不超过 30 ⼈。会议通过领域简介、头脑⻛暴、焦点问题等交流形式,辅之轻松愉悦的⾃由讨论和休闲活动,期望孕育复杂系统研究的原创性想法和思路。
本次研讨会与诸多会议不同之处在于:1)高度交叉(数学、物理、信息、⽣命领域);2)高度聚焦(⾃由能、熵等基于热⼒学语⾔和框架所刻画的复杂、⾮平衡态系统);3)高度联动(会议单元并非每⼈介绍本⼈⼯作,而是以跨学科/领域的共同概念为基础的讨论、协同与互动)。研讨会可看成是⼀场在轻松休闲⾃然环境下持续多⽇的团队攻关 collective problem solving,会议宗旨是希望凝聚出复杂智能系统和过程的奠基性原理和⽅程。除了安排⼏场基础背景介绍的报告之外,其余时间以头脑⻛暴和聚焦攻关的形式。根据需要,在会议期间会临时调整议题,也会有参会者的即兴报告和汇报 presentation。 为保障质量,研讨会采⽤邀请制:参会⼈员是认可会议宗旨的在本领域具有相当基础和语⾔的专家和少数有潜⼒的学⽣。
SIMIS-TSIMF INTERDISCIPLINARY SERIES International Workshop on Logic, Cognition, and Philosophy of Mathematics
会议编号:
M240403
时间:
2024-04-29 ~ 2024-05-03
浏览次数:
240
This workshop will bring together experts in logic, philosophy, mathematics, and cognitive sciences to discuss pioneering topics at the intersections of their fields. Key areas of focus will include the exploration of Kripke and topological semantics in modal logic, the examination of neighborhood semantics, and the integration of logic with game theory and graph theory. Participants will look into the implications of these topics for cognitive science, fostering a collaborative environment for advancing interdisciplinary research.
Workshop Format This invitation-only workshop will be organized in a "Daghstrul" style, which promotes a free and dynamic environment for discussions, interactions, and collaborations. This format will allow participants to engage deeply with various focused topics through informal and fluid session structures. Such an approach is designed to foster innovative solutions across the interdisciplinary fields involved.
SPDEs and multiscale analysis
会议编号:
M240402
时间:
2024-04-12 ~ 2024-04-14
浏览次数:
639
2024年4月11日-14日,由清华大学丘成桐数学科学中心荆文甲老师,华中科技大学高婷老师,北京雁栖湖应用数学研究院张琦老师组织的随机偏微分方程与多尺度分析研讨会(SPDEs and multiscale analysis)将在清华三亚国际数学论坛如期举行,本次会议共有24位(含线上)来自国内数所院校或研究机构的数学学者参加,会议期间将探讨有关随机偏微分方程与多尺度分析等相关研究问题。共有22场相关学术报告。
Elliptic Discrete Integrable Systems
会议编号:
M240401
时间:
2024-04-08 ~ 2024-04-12
浏览次数:
1072
会议摘要(Abstract)
Elliptic discrete integrable systems are among the richest of the whole class of integrable equations, both continuous as well as discrete. Their solutions in terms of special functions involve novel features, such as bi-elliptic addition formulae and elliptic generalisations of classical functions and orthogonal polynomials. A lot of progress have been made on various aspects of the theory, but some important elliptic models have received not as much attention as they deserve. One of the aims of the workshop is to repair this inbalance. Thus, the workshop will bring together experts who have worked on various aspects of integrability and elliptic function theory, and thus aim at bringing progress in dealing with these challenging but rewarding model systems.
在整个连续和离散可积方程中,椭圆离散可积系统被认为蕴含着最为丰富的信息。关于这类系统的求解,涉及到特殊函数的一些新的性质,如双-椭圆加法公式、经典的函数与正交多项式的椭圆推广等。对于椭圆离散可积系统理论的研究在许多方面都取得了不小的进展,但一些重要的椭圆可积模型尚未获得应有的关注。这也是此次研讨会的举办背景之一。研讨会将汇集可积系统和椭圆函数理论各个方面的专家学者,交流在这些具有挑战性的可积模型方面的研究进展,发展相关理论。
举办意义(Description of the aim)
Elliptic integrable systems are, in principle, exactly solvable model equations defined through ordinary or partial difference equations and that contain parameters associated with an elliptic curve. In the continuous case the outstanding examples are the Krichever-Novikov equation and the fully anisotropic Landau-Lifschitz equation, where in the former case the equation contains an arbitrary quartic polynomial in the dependent variable, to which one can associate an elliptic curve, while in the latter case the anisotropy parameters in general position are associated with the moduli of an elliptic curve. The discovery of discrete analogues of these equations and their significance within the framework of integrable systems forms the main motivation for this proposal. In addition, classes of ordinary difference equations of discrete-time many-body systems exhibit features which are radically different and richer than those of the corresponding continuous-time many-body systems. (Recently a novel example of such an elliptic many-body system arising as reduction of the BKP equation was found by Zabrodin). Furthermore, there is an entire classification of difference equations of Painlevé type (i.e. equations whose general solutions are meromorphic w.r.t. the movable singularities) at the top of which stands the elliptic Painlevé equation discovered in 1999 by H. Sakai. About a year earlier V. Adler discovered a discrete analogue of the Krichever-Novikov equation, which stands at the top of the well-known Adler-Bobenko-Suris (ABS) classification of quadrilateral lattice equations, which are four-point partial difference equations integrable in the sense of being multidimensionally consistent (i.e., consistently embeddable in a higher-dimensional lattice). Regarding the Landau-Lifschitz equations, there are three independent versions known: one proposed by Nijhoff and Papageorgiou in 1989, another constructed by Adler and Yamilov in 1996, and yet a third proposed by Adler himself in 2000. Almost nothing is known to date about these three models, not even if/how they are interrelated. Nonetheless, it would be of great interest to know their solution structures and their connection with other integrable systems. Finally, there is also a three-dimensional system of equations, namely an elliptic version of the Kadomtsev-Petviashvili equation, which was first proposed by Date, Jimbo and Miwa in 1983 and further studied recently by Fu and Nijhoff.
Apart from elliptic models, there are also classes of elliptic solutions of integrable lattice equations that exhibit novel features, such as a new concept of elliptic Nth root of unity, appearing in elliptic solutions of higher rank lattice equations of Gel’fand-Dickey type.
There are many outstanding problems in the theory of elliptic discrete systems, and resolving them has become urgent, as they stand at the top of the tree of integrable systems: knowing their resolution would imply the resolution of similar questions for the degenerate cases, which comprises almost all integrable equations.
In recent years, various novel mathematical techniques and methods have been developed to study these discrete systems and their solutions, bringing together ideas stemming from several branches of mathematics and physics, that are usually distinct, now come together: asymptotic analysis, algebraic geometry, representation theory, spectral/isomonodromy analysis, random matrix theory, exactly solvable models, theory of special functions and combinatorial geometry. These will form the unifying themes of the workshop, which will comprise the following topics:
--Elliptic solutions of higher-rank and multidimensional lattice equations;
--The construction of higher-rank elliptic lattice systems;
--Bi-elliptic addition formulae (as appearing in the soliton solutions of the ABS Q4 equation);
--Elliptic discrete time many-body systems;
--The solution structure of the variants of the lattice Landau-Lifschitz equations;
--Elliptic Lax pairs and isomonodromic deformation problems;
--Elliptic orthogonal polynomials and corresponding elliptic discrete integrable systems;
--Reductions to elliptic autonomous and non-autonomous ordinary difference equations, such as the QRT map and elliptic Painlevé equation;
--Algebro-geometric solutions of integrable lattice equations, and higher-genus lattice systems;
--Elliptic solutions of recurrence relations for integer (Somos) sequences;
--Connections with models of quantum theory and statistical mechanics.
椭圆离散可积系统指包含与椭圆曲线相关的参数的精确可解的常差分方程或偏差分方程。在连续情况下,典型的例子是Krichever-Novikov方程和各向异性Landau-Lifschitz方程。前者方程中包含有关于因变量的任意四次多项式,可以将椭圆曲线与之关联;而后者涉及的各向异性参数与椭圆曲线的模参数相关。这些方程的离散形式的发现及它们在可积系统框架内具有的重要意义构成申请此次研讨会的主要背景。在描述离散时间的多体系统的常差分方程中表现出与相应的连续时间多体系统截然不同且更丰富的性质。最近,Zabrodin给出了一个从BKP方程约化获得椭圆多体系统的新例子。目前关于Painlevé型 (即其通解相对于可移动奇点是亚纯函数的方程) 差分方程已有完整的分类,分类中处于顶端的方程是1999年由H. Sakai发现的椭圆离散Painlevé方程。大约在Sakai的工作的一年之前,V. Adler发现了Krichever-Novikov方程的离散形式,该方程处于后来给出的Adler-Bobenko-Suris (ABS)著名的关于多维相容的四边形方程分类的顶端 (多维相容性定义了一种离散可积性,指低维方程可以相容地嵌入到更高维空间)。关于Landau-Lifschitz方程,目前有三个已知的独立的离散版本:一个由Nijhoff和Papageorgiou于1989年提出,一个由Adler和Yamilov于1996年构建,还有一个由Adler于2000年给出。迄今为止,人们对这三个离散的Landau-Lifschitz模型知之甚少,甚至还不清楚它们之间是否存在联系或如何关联。十分期待理解它们的解结构以及它们与其他可积系统的联系。最后,还有一个与Kadomtsev-Petviashvili方程相关的椭圆三维方程组,由Date、Jimbo和Miwa于1983年提出,最近由Fu和Nijhoff对其做了进一步研究。
除了椭圆模型以外,离散可积方程还存在多种类型的椭圆函数解,并涉及到一些新的特征。例如在Gelfand-Dickey型高阶离散方程的椭圆孤子解的研究中引入了新的“椭圆单位根”的概念。
椭圆离散系统理论中存在许多尚未解决且亟待研究的问题。发展椭圆可积系统的研究方法具有重要意义。事实上,椭圆可积系统处于可积系统分类的顶端,这类系统通过退化几乎包括了所有的可积方程。
近年来,不断有新的数学技巧和方法出现,用于研究这类系统及其精确解。这些研究逐步将来自于数学和物理的若干看似不同的分支结合起来,包括:渐近分析、代数几何、表示理论、谱/等单值性分析、随机矩阵理论、精确可解模型、特殊函数理论和组合几何等。这些贯穿于此次研讨会的主题内容,具体地,我们将关注:
--高阶和高维离散方程的椭圆函数解;
--高阶椭圆离散系统的构造;
--双-椭圆加法公式(出现于ABS的Q4方程的孤子解中);
--椭圆离散多体系统;
--各种离散Landau-Lifschitz 方程的解的结构;
--椭圆Lax 对和等单值形变问题;
--椭圆正交多项式与相应的椭圆离散可积系统;
--椭圆自治与非自治常差分方程的约化,如QRT映射与椭圆Painlevé方程;
--离散可积系统的代数几何解与高亏格离散系统;
--整数(Somos)序列的递推结构的椭圆解;
--量子理论模型与统计力学方面的联系。
2024年4月11日-14日,由清华大学丘成桐数学科学中心荆文甲老师,华中科技大学高婷老师,北京雁栖湖应用数学研究院张琦老师组织的随机偏微分方程与多尺度分析研讨会(SPDEs and multiscale analysis)将在清华三亚国际数学论坛如期举行,本次会议共有24位(含线上)来自国内数所院校或研究机构的数学学者参加,会议期间将探讨有关随机偏微分方程与多尺度分析等相关研究问题。共有22场相关学术报告。
2024年1月8日-1月12日,三亚波国际前沿论坛(Sanya Waves)学术会议将在清华三亚国际数学论坛如期举行,本次会议共有62位来自国内数所院校或研究机构的数学学者参加,会议期间就非线性波动方程、几何分析和广义相对论等基本问题展开研讨,共有19场相关学术报告。
2024年1月7日-1月13日,由新加坡国立大学力学工程系助理教授、中国科学技术大学近代力学系刘难生教授、香港城市大学数学系胡先鹏教授组织的粘弹性流体的动力学:从理论到机理(Viscoelastic Flow Dynamics: from Theory to Mechanisms)学术会议将在清华三亚国际数学论坛如期举行,本次会议共有49位来自国内数所院校或研究机构的数学学者参加,会议期间就粘弹性流体相关的数学研究及其物理机理展开研讨,共有35场相关学术报告。
2023年7月22日-7月29日,由清华大学郑建华、南昌大学曹廷彬、华南师范大学黄志波老师组织的“复动力系统与复方程研讨会(Workshop on Complex Dynamics and Complex Equations)”学术会议在清华三亚国际数学论坛如期举行,本次会议共有42位来自国内数所院校或研究机构的数学学者参加。
2023年3月31日-4月4日,由华中师范大学凡石磊、中国科学院刘劲松、清华大学吴云辉和浙江大学叶和溪老师组织的2023“动力系统,Teichmuller理论及相关主题”学术会议(Dynamics, Teichmuller theory and their related topics)将在清华三亚国际数学论坛如期举行,本次会议共有76位来自国内数所院校或研究机构的数学学者参加,会议期间就动力系统,Teichmuller理论及相关主题展开研讨,届时将举行28场相关学术报告。
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