2024-03-18 ~ 2024-03-23
2024-03-04 ~ 2024-03-08
2024-02-19 ~ 2024-02-23
2024-02-19 ~ 2024-02-23
2024-02-15 ~ 2024-02-19
The interaction between geometry, quantum field theory and nonlinear analysis
会议编号:
M240302
时间:
2024-03-18 ~ 2024-03-23
浏览次数:
493
会议摘要(Abstract)
The interaction between geometry (Riemannian, algebraic, Kaehler, metric,...), quantum field theory and analysis (elliptic and parabolic PDEs, calculus of variations) has brought spectacular advances and generated deep insight in all those disciplines.
Minima of variational integrals may provide optimal solutions to geometric problems, and parabolic PDEs may deform initial geometrical structures into optimal ones, thereby solving important geometric problems. Functionals from QFT contain rich structures that can be exploited for the construction of subtle geometric invariants. In turn, such problems typically lead to very difficult analytical challenges. The resulting PDEs are not only highly non-linear, but from a variational perspective usually are not contained in the range of the Palais-Smale condition, and therefore, standard methods usually break down. This challenge gave an important impetus to the theory of non-linear PDEs. One line of research exploited convexity properties, typically arising from non-positive curvature, another one depended on an extremely careful study of the formation of singularities, which in turn had to use geometric features or algebraic properties from QFT.
During this workshop, we want to bring people together to explore various current research questions in this field, including
-- Analytic methods for studying moduli spaces in algebraic geometry
-- A general mathematical theory of the action functionals of QFT and the resulting challenges for PDE theory to construct minimizers or other critical points and to understand their regularity properties
-- Relations between QFT functionals and geometric constructions, like Kapustin-Witten and Higgs fields
-- Bernstein and Dirichlet problems for minimal submanifolds of Euclidean spaces and spheres
-- The role of PDEs in metric space geometry
-- The geometry of positive sectional curvature
-- The approximation of geometric objects by discrete ones
我们希望通过本次研讨会组织与会者一起探讨几何、量子场论和分析相互作用领域的前沿问题,包括:
-- 代数几何中模空间的分析方法;
-- 量子场论中作用泛函的一般数学理论及产生的偏微分方程理论挑战,如构造极小解或其它临界点,研究它们的正则性;
-- 量子场论中作用泛函与几何构造的关系,如Kapustin-Witten 和 Higgs 场;
-- 欧氏空间和球面中极小子流形的Bernstein 和 Dirichlet 问题;
-- 偏微分方程在度量空间几何中的作用;
-- 正曲率几何学;
-- 几何对象的离散逼近。
举办意义(Description of the aim)
几何,量子场论和非线性分析之间的相互作用为这些领域中带来了巨大的推动和深刻的洞察。变分问题的极小点为几何问题提供了最优解,抛物方程把初始几何结构形变为最优解,从而解决重要的几何问题。量子场论中的作用量泛函包含丰富的结构,可以用于构造精妙的几何不变量。反之,这些问题也常常带来困难的分析挑战,其产生的偏微分方程不仅是高度非线性的,而且从变分观点看通常不能包含在满足Palais-Smale条件的范围中,因此,标准的方法往往失效。这种挑战为我们提供了发展非线性分析理论的重要动力,一条途径是运用凸性性质,常见于非正曲率情形,另一条途径是依赖于对奇性形成的精细研究,这反过来需要利用量子场论的几何特性或代数性质。在本次研讨会期间,我们将探讨有关几何,量子场论和非线性分析之间相互作用领域的前沿研究问题。
Advanced Finite Elements Methods for Nonlinear PDEs
会议编号:
M240301
时间:
2024-03-04 ~ 2024-03-08
浏览次数:
741
会议主题(Theme)
本次会议以“非线性偏微分方程的高效有限元方法”为主题,针对科学与工程计算中的非线性偏微分方程,研究其高精度有限元方法。会议拟邀请50位国内外相关领域中的杰出学者,开展学术报告和交流合作。此次会议将极大增进非线性问题数值解法的前沿研究和发展趋势的交流与讨论,为青年学者开拓学术视野,创造合作机遇。
The theme of this meeting is "Advanced Finite Element Methods for Nonlinear PDEs", focusing on high-precision finite element methods for nonlinear partial differential equations in scientific and engineering calculations. The conference plans to invite 50 outstanding scholars from relevant fields both domestically and internationally to conduct academic presentations, exchange and cooperation. This conference will greatly enhance the exchange and discussion of cutting-edge research and development trends in numerical solutions for nonlinear problems, broaden academic horizons for young scholars, and create opportunities for cooperation.
举办意义(Description of the aim)
非线性偏微分方程的数值求解是一个既有广泛工程应用背景,又具有挑战性的困难课题。连续力学中变分形式的强非线性问题,协调有限元离散可以把原问题归结为极小值的数值计算问题,而对于一般的非变分形式的强非线性偏微分方程,如 HJB 方程,离散过程并不是那么简单。本次会议主旨是把变分计算专家和非变分形式微分方程数值解学者聚集起来,针对非线性问题的数值求解展开合作研究和讨论。本次会议的议题涉及非线性问题数值解法的前沿研究,具有重要的实际意义。
The numerical solution of Nonlinear partial differential equation is a difficult subject with both extensive engineering applications and challenges. For the strongly nonlinear problems in the variational form of continuous mechanics, the original problem can be reduced to the numerical calculation problem of the minimum by the coordinated finite element discretization, while for the strongly nonlinear partial differential equations in the general non variational form, such as the HJB equation, the discretization process is not so simple. The main purpose of this meeting is to gather experts in variational computation and numerical solvers of non variational form differential equations to conduct collaborative research and discussion on numerical solutions for nonlinear problems. The topic of this meeting involves cutting-edge research on numerical solutions for nonlinear problems, which has important practical significance.
Modern Aspects of Quantum Field Theory
会议编号:
M240203
时间:
2024-02-19 ~ 2024-02-23
浏览次数:
1142
会议摘要(Abstract)
The goal of this workshop is to bring together renowned local and international experts on modern aspects of quantum field theory for talks and discussions. The range of topics covered will include Anomalies, Scattering Amplitudes, Categorical Symmetries, GLSMs and Mirror Symmetry, Supersymmetric Localization, and Instanton partition functions.
举办意义(Description of the aim)
The aim will be to give participants a global view on current developments in quantum field theory and encourage cross-field interactions and connections.
Working Seminar on Analytic Number Theory
会议编号:
M240202
时间:
2024-02-19 ~ 2024-02-23
浏览次数:
1042
会议报名已截止-Conference registration is closed.
会议主题(Theme)
本次会议以自守形式的解析理论为主题,关注它在现代解析数论中的发展。主要涉及自守形式与Kloosterman和的谱理论、高阶L函数的Riemann假设与Lindelof假设以及自守形式解析理论的应用(如QUE猜想、素测底线定理以及二次型的算术等)。
会议主要邀请国内积极活跃的年轻学者,他们长期从事自守形式与现代解析数论的研究,在L函数的亚凸界、均值及其算术应用等方面做出了贡献。主讲人分工讲解若干篇经典的重要文献,讲解注重思想并力求细致,且重要阐述与之相关的历史背景、发展现状及相关研究课题。计划涉及的主题及文献主要包括:
[1] J. Conrey, H. Iwaniec, The cubic moment of central values of automorphic L-functions, Ann. of Math. 151 (2000), 1175-1216.
[2] J.-M. Deshouillers, H. Iwaniec, Kloosterman sums and Fourier coefficients of cusp forms, Inventiones math. 70 (1982), 219-288.
[3] W. Luo, P. Sarnak, Quantum ergodicity of Eigenfunctions on PSL2(Z)\H2, Publ. Math. IHÉS 81 (1995), 207-237.
[4] Y. Motohashi, An explicit formula for the fourth power mean of the Riemann zeta-function, Acta Math. 170 (1993), 181-220
[5] I. Petrow and M. P. Young. The Weyl bound for Dirichlet L-functions of cube-free conductor. Ann. of Math. 192 (2020), 437-486.
举办意义(Description of the aim)
解析数论在过去的几十年中取得了蓬勃的发展,既包括与素数分布相关的若干经典问题,还涉及与自守表示及代数几何等分支深度交叉融合的现代理论。
本次活动主要面向国内从事数论研究的青年学者、研究生及部分高年级本科生,一方面助其打下相关的专业基础,另一方面鼓励不同背景的研究人员深入开展合作研究。
活动的举办必将大力推动现代解析数论在国内的进一步生长与发展。
Workshop on Mathematics, Image Science and Artificial Intelligence (MISAI)
会议编号:
M240201
时间:
2024-02-15 ~ 2024-02-19
浏览次数:
1831
会议主题(Theme):
本次会议以“数学、图像科学和人工智能”为主题,旨在探讨数学、图像科学与人工智能之间的学科交叉问题,分享最新的研究成果和技术进展,并为相关领域的研究人员提供一个交流和合作的平台。
The theme of this conference is "Mathematics, Image Science and Artificial Intelligence", aiming to explore the interdisciplinary problems among mathematics, image science, and artificial intelligence, share the latest research achievements and technological advancements, and provide a platform for communication and collaboration among researchers in relevant fields.
会议议题(Agenda):
1)数学理论和方法在图像分析和处理中的应用;
2)深度学习和神经网络在图像分类和识别中的应用;
3)计算机视觉和机器人技术;
4)自然语言处理和机器翻译;
5)数学建模和仿真在人工智能中的应用。
1) Mathematical theories and methods for image analysis and processing;
2) Deep learning and neural networks for image classification and recognition;
3) Computer vision and robotics;
4) Natural language processing and machine translation;
5) Mathematical modeling and simulation in artificial intelligence.
举办意义(Significance):
举办这次会议的意义在于促进数学、图像科学和人工智能领域的学科交叉研究,推动学术界和产业界在这些领域的合作和交流,促进跨学科交流与合作。同时,这次会议有助于促进数学、图像科学与人工智能领域的学科交叉人才的培养,推动这些领域的理论与技术发展,提高学术研究水平和技术应用能力。
The significance of organizing this conference is to promote interdisciplinary research among mathematics, image science, and artificial intelligence, facilitate cooperation and communication between academia and industry in these fields, and encourage interdisciplinary exchange and collaboration. Additionally, this conference can contribute to the cultivation of interdisciplinary talents in the fields of mathematics, image science, and artificial intelligence, advance the development of theory and technology in these fields, and enhance the academic research level and technical application abilities.
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。
由丘成桐(清华大学)、Will Donovan(清华大学)、Mauricio Romo(清华大学)、郑璐予(清华大学)组织的红外同调代数研讨会(Homological Algebra of the Infrared)将于1月8-14日在清华三亚国际数学论坛召开。
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参会人员
学术报告
国际数学会议