会议摘要（Abstract）

本次会议的主题是探讨如何通过数学工程以及数据驱动的方法来解决复杂的工程问题。数学工程是运用数学方法解决工程难题的学科，它基于数学定律，这些定律不仅可以描述许多物理和自然现象，也适用于解决多种工程问题。

近年来，随着新兴工程领域的快速扩展，特别是在信息生成与管理领域，对工程问题进行原创性数学分析的需求大幅增加。我们使用的系统变得愈加复杂，许多领域需要运用更加智能化的手段，包括信息的收集、评估、分析以及从中得出结论并实施有效控制。这种复杂性促使我们开发出更加精细的数学工具和方法，以应对这些挑战。

在现代社会中，许多领域都迫切需要新的数学方法，例如大数据处理、传感器网络、深度学习、自动化系统以及大规模的环境建模等。在这些领域中，数学工程的核心工作是首先开发出有效的模型，随后通过合适的数学工具处理这些模型，并引导它们的演化过程。自动驾驶技术就是其中的一个典型例子。尽管该技术取得了长足进展，但目前自动驾驶的认知能力还远远无法与人类驾驶员相媲美。自动驾驶系统的可靠性仍然落后于人类驾驶员，差距甚至高达1000倍，缩小这一差距将需要在数学领域进行重大的技术创新和研究。

此次研讨会邀请了一批以研究为导向的工程专家和应用数学专家，他们当中有许多是这一重要领域的开拓者。与会者将通过交流思想、分享经验和探讨前沿问题的解决方案，共同推动数学工程领域的进一步发展。

The topic of this conference is the application of mathematical engineering to solve complex engineering problems using mathematical methods and data-driven methods. Mathematical engineering is the art of solving engineering problems using mathematical means. Mathematical laws characterize many physical and natural phenomena. The same holds for many engineering problems.

The need of original mathematical analysis of engineering problems has greatly increased in recent times, in parallel with the massive development of new engineering fields, especially in the very wide area of information generation and management. The rapid increase in the complexity of the systems we use, and the need to use more refined intelligence (such as the ability to gather information, evaluate it, derive conclusions from observations and putting in place effective controls) in a large variety of areas requires the development of more refined mathematical means.

Modern fields of endeavor requiring novel mathematical efforts include the handling of large data sets, sensor networking, deep learning, autonomous systems, large scale environmental modeling, and many more. In all these cases, mathematical engineering starts out with the development of effective models (the accurate but simple modeling of engineering phenomena is a major issue in itself), followed by the development of adequate mathematical tools to handle the models and to steer their evolution. This process is perhaps best exemplified by autonomous driving, which still has a long way to go before it can rival the cognitive abilities of a driving human (the reliability of an automatic car driver is still a factor of a thousand off mark, and it will require major mathematical effort to solve just this problem).

 This conference assembles a limited number of research-oriented engineers, many of them among the pioneers in the development of this crucial field, and who want to exchange their ideas, present experiences and share views on how to deal with novel problem challenges in the field.

举办意义(Description of the aim)

本次国际会议汇聚全球工程学与应用数学领域的顶尖专家，聚焦数学与数据驱动方法在复杂工程问题中的创新应用。会议旨在搭建跨国界、跨学科的高端交流平台，推动知识共享与技术协作，加速相关领域的前沿突破。

随着信息科学领域工程技术的飞速发展，对数学建模与分析的需求持续攀升。面对大数据流实时处理、传感器网络效能评估、自主控制系统开发等关键课题，亟需先进技术手段支撑。本届会议将系统探讨最前沿方法体系，重点解析其在真实工程场景的转化路径与支撑效果。

主要议题包括大数据集、传感器网络、深度学习、控制系统和环境建模中的开放难题。数学工程在解决上述难题中发挥双重作用：一方面正确构建工程现象数学模型，另一方面利用前沿应用数学工具解决模型对应的工程领域中的开放难题。本次会议也将包括自动驾驶等专题研讨，通过具体领域典型案例展示数学方法如何解决前沿难题。

通过此次会议，我们旨在推动数学工程学科理论体系的完善，推动更深入的国际合作，并为应用数学界与工业界提供一个沟通交流的平台。

This international conference gathers world-class experts in engineering and applied mathematics to address the challenges of solving complex engineering problems using mathematical and data-driven methods. It serves as a platform for fostering collaboration and exchanging cutting-edge knowledge, bringing together both domestic and international participants to drive innovation and advance research in this field.

Recent advancements have heightened the demand for innovative mathematical analysis, particularly in the areas of information generation and management. The ability to efficiently handle large data flows, evaluate sensor networks, and develop autonomous systems requires advanced techniques. This conference will explore these state-of-the-art methods, focusing on their applications across various engineering domains.

Key topics include the challenges of managing large data sets, sensor networks, deep learning, autonomous systems, and environmental modeling. Mathematical engineering plays a vital role in these areas, starting with the development of models that simplify engineering phenomena and continuing with the creation of tools to manage these models effectively. Autonomous driving will be highlighted as a prime example, where mathematical advancements help bridge the gap between human and machine performance.

Through this conference, we aim to significantly contribute to the development of mathematical engineering, promoting deeper international collaboration and creating opportunities for innovation that will benefit both academia and industry.

Abstract 

Description of Activity 

We propose the 7th TSIMF Conference on Computational and Mathematical Biophysics and Bioinformatics to be held at Tsinghua Sanya International Mathematics Forum (TSIMF) in the December 2025.  

Rationale 

The proposed workshop on “Computational and Mathematical Biophysics and Bioinformatics” will bring together researchers from mathematics, biostatistics, chemistry, biochemistry, biophysics, and molecular/cell biology to explore new ways to bridge these diverse disciplines, and to facilitate the use of mathematics to solve open problems at the forefront of the biophysics and bioinformatics. 

An important trend in contemporary life sciences is that with the availability of modern biotechnologies, traditional disciplines, such as physiology, plant biology, neuroscience etc., are undergoing a fundamental transition from macroscopic phenomenological ones into molecular based biosciences. In parallel with this development, a major feature of life sciences in the 21st century is their transformation from phenomenological and descriptive disciplines to quantitative and predictive ones. Revolutionary opportunities have emerged for mathematically driven advances in biological research. Experimental exploration of self-organizing molecular and cellular biological systems, such as SARS-CoV-2, molecular motors and proteins in Alzheimer's disease, are examples of dominating driving forces in scientific discovery and innovation in the past few decades. However, the emergence of excessive complexity in self-organizing biological systems poses fundamental challenges to their quantitative description, because of the excessively high dimensionality and the complexity of the processes involved. Mathematical approaches that are able to efficiently reduce the number of degrees of freedom, and model complex biological systems, are becoming increasingly popular in biosciences. Multiscale modeling, manifold extraction, sequencing analysis, topological simplification, dimensionality reduction and machine learning techniques are introduced to reduce the complexity of biological systems while maintaining an essential and adequate description of the molecules and cells of interest. 

Scope 

The workshop will cover a wide range of topics in mathematical modeling of biophysics and bioinformatics, and their applications to specific research problems. Example topics include comparative analysis of human genome and molecular evolution, mechanism of bacterial drug resistance, genome variation polymorphism, genome correlation of important diseases, single-cell sequencing analysis, high-throughput gene sequencing analysis, differential geometry based multiscale models, topological simplification of biomolecules, GLMY homology, natural vectors, Yau-Hausdorff distance, geometric algebra, knot theory of DNA, RNA and proteins,  implicit solvation models, Poisson-Boltzmann equation, generalized Born models, polarizable continuum models, integral equation models, density functional methods, Poisson-Nernst-Planck equations, Micro-macro models, continuum-discrete models, microfluidics, biomolecular transport, multiscale Brownian dynamics, electrokinetics, electrohydrodynamics, quantum mechanics, molecular mechanics, and  coarse-grained models. Emphasis will be placed on the application of the aforementioned models, theories and methods to precision medicine, early warning of virus and microorganism disasters, large data database construction and retrieval technology for genomic, proteomic, spatiotemporal single-cell transcriptomic data processing, pharmaceutical software technology, DNA packing, DNA-protein interaction, protein-protein interaction, protein-ligand interaction, mathematical AI for biosciences, topological deep learning for biosciences, single-cell RNA sequence analysis, spatial transcriptome data, multiomic analysis, ion channel dynamics, ionic transport in nanopore membranes, rational drug design, drug discovery and delivery, macromolecular self assembly and dynamics of molecular motors.   

Description of the aim 

Objectives 

• To develop multiscale mathematical models that can effectively utilize current computational capabilities.

• To advance our understanding of the complexity of human genome and biomolecular structure, function, dynamics, and transport.

• To foster new ties, interaction and collaboration between mathematicians, bioinformatics scientist, biophysicists, and molecular biologists.

• To provide a forum to exchange ideas and results related to research in bioinformatics and biophysics.

• To help stimulate information flow of “biology to mathematics”, i.e., to introduce new bio-inspired mathematical models to graduate students and recent doctoral recipients in biology.

• To introduce the field and subject to graduate students, postdocs and junior faculty members, and help training the next generation researchers in the field.

• To enhance the participation of women, under-represented minorities, and persons with disabilities in the research of molecular based mathematical biology.

Impact 

Currently, a major barrier for mathematical scientists to work in biophysics and bioinformatics is the lack of knowledge in molecular and cellular biology, while a major barrier for biologists is the lack of knowledge about modern mathematical tools and techniques that have been developed in the past few decades. This workshop series is designed to help bridge gaps between biologists and mathematical scientists and to facilitate their collaborations. There is enormous potential in this area for integrative interdisciplinary research in which theoreticians and experimentalists develop solutions to challenging problems in tandem. This workshop series will act as a catalyst to fully exploit these synergies, and create a network of collaborations that will sustain future activities in this area beyond the duration of this workshop. 

Previous Achievements 

The TSIMF annual workshop series on “Computational and Mathematical Biophysics and Bioinformatics” has been successfully held for six times from 2018 – 2024. Four workshops were in-person events and took place at the Sanya, while the third and fourth workshop was held online through the Zoom in Dec. 2020 and Dec. 2021, respectively.  

To record these CMBB workshops, five special issues have been published from 2018 – 2024 in the journal: Communications in Information & Systems (CIS) 

https://www.intlpress.com/site/pub/pages/journals/items/cis/_home/_main/index.php.  

The numbers of papers published in these five special issues are 6, 10, 7, 5, and 7 respectively. The special issue for the sixth workshop will be published in the CIS in 2025.  

These previous CMBB workshops and the associated special issues have attracted more people from mathematics and biology to work on the modeling and computation of biophysics and bioinformatics, and fostered further collaborations among them. Based on our previous successful achievements, we are confident that the proposed TSIMF workshop series will stimulate new research directions in mathematics and computation to address fundamental challenges in biophysics and bioinformatics. 

Number of Participants 

In the preliminary list of proposed participants below, we have listed more than 50 people. Please note that not every invitee will accept the invitation. Moreover, the first come and first serve principle will be applied so that we can guarantee that the number of participants will not exceed 50.   

Abstract 

This symposium, organized by Tsinghua University and the Beijing Institute of Mathematical Sciences and Applications (BIMSA), and co-organized by the Institute of Mathematics for Industry (IMI), Kyushu University, and the Faculty of Mathematics and Information Sciences, Warsaw University of Technology, aims to bring together experts from various domains of singularity theory, its applications, and computational intelligence to discuss cutting-edge research developments. The conference will focus on algebraic and geometric approaches to singularity theory, including but not limited to singularities of smooth maps and differential forms, Lipschitz stratifications, symplectic singularities, local invariants, topology of singularities, Hamiltonian systems and their generalizations, and singularities in algebraic geometry. Additionally, the symposium will highlight the crucial role of mathematics in industry, computational intelligence, and nanoscale sciences, particularly nanomedicine, emphasizing mathematical modeling, simulation, and data analysis in interdisciplinary research. Featuring keynote speeches and thematic sessions, the event establishes a cross-disciplinary exchange platform to foster deeper integration between mathematical theories and computational sciences.  

Description of the aim 

The aim of the symposium is to bring together specialists of various domains of singularity theory its applications and computational intelligence. The field of computational intelligence is breaking records in popularity. We are seeing its progress in both new fields of application and ever-improving algorithms. At the intersection of mathematics and computer science, an area of knowledge has emerged that can be said to affect (almost) everyone and is difficult to pass by indifferently. At the meetings of the Symposium, we expect, in this direction, to address issues such as data representation,new methods of computational complexity and many others. We expect invited talks represent various approaches, algebraic and analytic to singularity theory problems based mainly on geometry. The topics are related to algebraic and geometric aspects of singularity theory and its related areas such as Singularities of smooth maps and differential forms, Subanalytic and semialgebraic sets, Lipschitz stratifications, Real algebraic aspects of singularities, Lagrangian and Legendrian singularities, Asymptotic behaviour around caustics and wavefronts, symplectic singularities, local invariants, Singular symplectic, contact and Poisson spaces, Local Algebras of singularities, resolution algebras, Hamiltonian systems and their generalizations, Differential geometry of singularities, Affine invariants of curves and surfaces. Free divisors, Torus actions, Topology of singularities, Singularities in positive characteristics and  singularities in algebraic geometry.  

The proposed Initiative aims also to highlight the importance of mathematics in industry, computational intelligence and nanoscale science, especially nanomedicine. The major role in the theoretical understanding of nanosized materials  is played by mathematics and computational methods. Both methods can provide effective theory and simulations for analysis and interpretation of experimental results, model-based prediction of quantitative and qualitative behaviour, and control of nanoscale systems. Mathematics also plays a vital role in the interaction of these different disciplines, since they all use data, simulation and visualization.  

We plan to use the conference to provide a good exchange platform on exciting new results on singularities and their applications and promote further the development of interactions of mathematical ideas and new branches of practical computational sciences. It is organized  with the special collaboration with IMI – Institute of  Mathematics for Industry, Kyushu University and Faculty of Mathematics and Information Sciences of Warsaw University of Technology. 

会议摘要（Abstract）

The modern theory of integrable systems, both classical and quantum, is well-known for its ability to provide unexpected connections between very different branches of mathematics and mathematical physics, such as representation theory, algebraic geometry, theory of special functions, and the list goes on and on. Many novel ideas in this field are motivated by questions in modern quantum field theory and string theory. 

The goal of the proposed workshop is to bring together world-class leading experts, on one hand, and talented young researchers and graduate students, on the other, to discuss some recent advances and ideas, with the emphasis on the use of algebro-geometric methods and techniques in the theory of integrable systems. Some of the key themes of the workshop are connections between cluster integrable systems and Painlevé equations, BPS/CFT correspondence, Fredholm determinants and tau-functions. 

We expect the workshop to provide a platform for an intensive exchange of ideas, updates on cutting-edge developments in the field, and creation of new research themes and international collaborations. To foster the latter, we plan to dedicate a significant amount of time to discussion sessions and open problem sessions.

举办意义(Description of the aim)

Background:

Over the past several decades, algebraic geometry and integrable systems have influenced each other in significant and mutually beneficial ways. On the one hand, techniques from algebraic geometry—such as the study of moduli spaces, spectral curves, and theta-functions—have provided deep structural insights into classical and quantum integrable models (e.g. the Krichever construction, Hitchin systems, the KP hierarchy and systems of interacting particles, spin chains). This includes construction of Lax pairs of integrable systems that can then be used to obtain exact algebro-geometric solutions of soliton equations, definition of Hitchin integrable systems arising from the moduli spaces of stable holomorphic bundles, powerful tools in studying Painlevé equations and Painlevé transcendents, and many others. Conversely, phenomena discovered in integrable systems, isomonodromic deformations, and Painlevé transcendents—have inspired new questions about the geometry of algebraic varieties, singularity theory, and mirror symmetry. Moreover, tau-functions of integrable hierarchies appear to be generating functions for many enumerative problems in algebraic geometry, such as Gromov–Witten invariants and Hurwitz numbers. The famous Novikov conjecture (Shiota theorem) characterizes the Jacobians of algebraic curves with the help of the KP hierarchy. Another important recent development is the application of algebraic geometry and integrable systems for a consistent formulation of a non-perturbative quantum field theories. One of the most important examples is the Seiberg–Witten theory for the low-energy effective actions and BPS states in the N=2 SUSY Yang-Mills theory in four macroscopic dimensions. It reformulates this close-to-realistic physical theory in terms of integrable systems and representation theory of infinite-dimensional algebras, while the non-perturbative transformations of the BPS spectra are governed by the cluster algebra relations.

Objectives:

This workshop will explore such interactions, highlighting both foundational results and emerging directions, such as

.cluster algebras and cluster integrable systems

.duality in integrable systems and algebraic geometry

.geometric theory of Painlevé equations

.isomonodromy transformations and tau functions

.BPS/CFT correspondence

.Lefschetz thimbles in QFT

This workshop will emphasize interactions between the world-leading experts and young researchers, including graduate students and postdocs, both from China and abroad. We expect that it would result in new and fruitful collaborations.

会议摘要（Abstract）

The topic of this workshop is the Hilbert module approach in operator theory, with an emphasis on the techniques of analytic function theory, complex geometry, and algebraic geometry. Operator theory, and more specifically, multivariable operator theory, and the aforementioned subjects share intimate connections. These subjects are closely related to a variety of disciplines, including PDE, operator algebras, linear analysis, and harmonic analysis, to mention only a few. The theory of operators evolved from the study of normal operators, Toeplitz operators, the Volterra operator, and index theory. A milestone is the Nagy-Foias analytic operator model theory developed in the 1950s and 60s, which states that every bounded linear operator can be represented as a compression of the shift operator to a certain Hilbert space of holomorphic functions. This fact reaffirms the algebraic link between traditional operator theory and function theory. Around the same time, index theory was given a topological, geometrical, and analytic framework in the deep work of Brown-Douglas-Fillmore, which in part motivated the development of noncommutative geometry. In light of these and other intriguing theories, it became clear that a more general framework is required to unify all the pertinent concepts. R. G. Douglas' introduction of Hilbert modules in the 1980s came at an opportune time. The theory makes available diverse tools and techniques from a wide range of fields, such as commutative algebra, complex geometry, several complex variables, and algebraic geometry, to name a few, for the study of operator systems and multivariable spectral theory. Indeed, with the passage of time, a great number of achievements have been made along this line, for example in the study of

 1) Cowen-Douglas operators,

 2) distinguished varieties (a concept introduced by Rudin),

 3) the interpolation problem,

 4) extension of analytic functions from algebraic variety,

 5) bounded symmetric domains,

 6) the Chevalley-Shephard-Todd theorem,

 7) the Riemann zeta function in terms of infinite polydisc,

 8) characteristic spaces.

Additional success has been recorded in the study of Samuel multiplicity, analytic K-homology, projective spectrum, bounded analytic functions, etc.

The theory of Hilbert modules has been very actively pursued since the last meeting on this subject, which took place at TSIMF shortly before the Covid pandemic. This proposed workshop aims to analyze the subject's evolution in recent years and outline possible future directions for growth. Particular attention will be given to early-career researchers. Indeed, a significant percent of the proposed participants are PhD students, postdocs, and tenure-track assistant professors. The proposed workshop will provide a good opportunity for them to communicate in-person and foster collaborations.

举办意义(Description of the aim)

The primary aim of the workshop is to provide a platform for the dissemination of recent research discoveries and to highlight the key challenges in the field of operator theory after reformulating them in the language of Hilbert modules. Over the past three decades, it has been amply clear that this reformulation is not merely a choice of language. It in fact creates a new landscape. For instance, submodules in several variable have complicated structure, and classifications of them become an appealing and yet rather challenging task. On the other hand, the study of quotient modules amounts to develop a multivariable Nagy-Foias model theory, which provides a fertile ground for the growth of multivariable operator theory.

The main themes of this workshop are as follows:

(A) Submodules and quotient modules over function algebras and the corresponding resolutions of Hilbert modules.

(B) Function theory on an infinite polydisc.

(C) The theory of bounded analytic functions in several variables and its connection to Hilbert modules.

(D) Multivariable spectral theory.

In terms of scientific goals, it is understood that function theory, multivariable operator theory, and the Hilbert module structure that goes with them depend heavily on the specific domain. The function theory of the open unit ball and that of the open unit polydisc, for example, differ significantly. Another emerging theory, as far as domain-related studies are concerned, is the Riemann zeta function in terms of function theory on an infinite polydisc. Indeed, the manner in which function theories vary across distinct domains is remarkable and fascinating. How these differences play a role in the study of Hilbert modules is worth serious investigation. It is undoubtedly a part of the allure of Hilbert modules and multivariable operator theory.

Another important subject concerns with essentially normal quotient modules. On infinite-dimensional Hilbert spaces, compact operators are the ``small'' objects that introduce numerical invariants, such as the index of a Fredholm operator. Self commutators [T, T*] and cross commutators [T_1, T_2*] of multiplication operators$T, T_1, and T_2 on Hilbert modules are often ``small'', prompting the question whether they are in fact ``smaller'', i.e., whether they belong to the so-called Schatten p-class. For homogeneous submodules in the Drury-Arveson space over the unit ball, this question is framed as the Arveson-Douglas conjecture, which has been a tantalizing open problem for some time. In fact, it is anticipated that the answer depends on the geometry of the zero variety of such submodules. This connection facilitates the study of analytic K-homology in an appropriate way. This workshop shall review the current status of the conjecture and investigate on recent novel approaches.

In addition to the aforementioned topics, the workshop also concerns with the following list of problems.

(i) The classification of submodules and quotient modules of analytic Hilbert modules.

(ii) Analytic and algebraic invariants of the submodules and quotient modules with respect to unitary equivalence, similarity, and quasi-similarity.

(iii) Investigating the essential normality of Hilbert modules, including the Douglas-Arveson conjecture mentioned above.

(iv) The problem of holomorphic imprimitivities as the restrictions of  imprimitivities in the sense of Mackey and its close connection with the subnormality of Cowen-Douglas modules.

(v) The problem of finding a complete set of invariants for holomorphic hermitian sheaves.

(vi) Interpolation on various domains and its consequences for Hilbert modules.

(vii) Spectral theory in the setting of Hilbert modules.

(viii) Beurling-Wintner dilation problem.

(ix) Szego's problem in infinite polydisc.

(x) Determinantal point process from multivariable operator theory. Undoubtedly, some of the aforementioned problems are complex and necessitate a long-term approach. We hope that this workshop will also help identify rising stars who might lead future efforts in addressing these challenges. Therefore, it will be in our best interest to invite a large number of young researchers to this workshop and foster their growth for the advancement of mathematics.

Previous Workshops: Some of the events that have taken place in the past few 15 years:

(i) Hilbert Modules in Analytic Function Spaces workshop,  Tsinghua Sanya International Mathematics Forum (TSIMF), Sanya, China, Dec 30, 2019 - Jan 3, 2020.

(ii) Hilbert Modules in Analytic Function Spaces workshop,  Tsinghua Sanya International Mathematics Forum (TISMF), Sanya, China, May 22-26, 2017.

(iii) Multivariate Operator Theory, BIRS, Banff, Canada, April 6 - 10, 2015.

(iv) Hilbert Modules and Complex Geometry, Oberwolfach, Germany, Apr 20- 26, 2014.

(v) Multivariate Operator Theory, BIRS, Banff, Canada, August 15 - 20, 2010.

(vi) Hilbert Modules and Complex Geometry, Oberwolfach, Germany, Apr 12- 18, 2009.