ICBS Lecture 国际基础科学大会报告

首届国际基础科学大会（International Congress of Basic Science,简称 ICBS）将于2023年7月16-28日在北京举行，主题为“聚焦基础科学，引领人类未来”。大会期间，约350场前沿科学奖报告（Frontiers of Science Award Lecture）、大会报告（Plenary Lecture）以及特邀报告（Invited Lecture）将在北京雁栖湖应用数学研究院举行。

11位中国科学院院士领衔主讲大会报告

东南大学

崔铁军

复旦大学

许宁生

中国科学院

邹冰松

香港大学

莫毅明

中国科学院

王贻芳

中国科学院

向涛

中国科学院

陈志明

中国科学院

吴岳良

中国科学院

张平

中国科学院

席南华

中国科学院

郭雷

7月17日-7月27日

Venue: TCIS Lecture Room 13 (A7 3F)

7月17日（星期一）下午 16:00-16:45

崔铁军 Tie Jun Cui

中国科学院院士、

东南大学信息科学与工程学院教授、

西安电子科技大学电子工程学院院长

Title

Information Metasurface – Simultaneous Modulations of Waves and Digital Information in Electromagnetic Space

Abstract

We proposed the concepts of digital coding metamaterial and metasurface, in which the meta-atoms are represented by using digital states of phases. The digital representation of metamaterial and metasurface makes it possible to manipulate the electromagnetic waves and modulate the digital information simultaneously on the same platform, evolving a new direction of information metamaterial and metasurface. The information metasurfaces set up a bridge between the physical world and the digital world. Integrated with field programmable gate array (FPGA), the information metasurfaces can control the electromagnetic waves and process the digital information in real time and programmable way. Based on the information metasurfaces, new-architecture microwave imaging and wireless communication systems have been designed and realized, showing great potentials in the next-generation wireless applications.

Venue: TCIS Lecture Room 13 (A7 3F)

7月18日（星期二）上午 09:15-10:15

许宁生 Ningsheng Xu

中国科学院院士、

发展中国家科学院院士、

曾任中山大学校长、复旦大学校长

Title

Nano science of the universe

Abstract

To raise issues of nano science of the universe. Currently studies have been focused on smaller and smaller scale nanomaterials around ourselves, and such scheme should be changed, and new research strategy will be proposed. Key issues to include the followings and beyond: i) nanomaterials exist in the universe and their synthesis mechanisms. ii) nanomaterials may lead to lives in the universe. iii) complex processes occurring in nano space of the universe.

Venue：Physics Lecture Room 4 (A3-2 1F)

7月18日（星期二）上午 10:30-11:00

邹冰松 Bingsong Zou

中国科学院院士、

中国科学院高能物理所研究员、

北京大学客座讲席教授

Title

Exotic hadronic states and hadron structure

Abstract

Hadrons, including mesons and baryons, are the smallest units that can be separated from matter and have been observed to have internal structures. Searching for new hadronic states and exploring their internal quark gluon structure is a cross cutting frontier topic of common concern in particle physics and medium to high energy nuclear physics. In recent years, more and more exotic hadronic states beyond the expectation of the classical Quark model have been observed experimentally. Although there are various explanations for their nature, these exotic hadron states can basically be explained as multi-quark hadronic molecular states. For hadrons that met the expectations of the Quark model in the past, such as protons, there are also some new experimental observations that cannot be explained by the classical Quark model, and the multi-quark component caused by the unquenching dynamics must be considered. Therefore, in order to truly understand the hadron spectrum and hadron structure, it is necessary to study multi-quark exotic hadron states.

Venue: Math Lecture Room 1 (A3-1 3F)

7月18日（星期二）下午 15:15-16:00

莫毅明 Ngaiming Mok

中国科学院院士、

香港科学院院士、

美国数学学会会士、

2022年获世界华人数学家大会陈省身奖得主、

香港大学数学研究所所长、

香港科学院副院长

Title

The Ax-Schanuel Conjecture on Shimura varieties

Abstract

In the subject of number theory, the classical Lindemann theorem, which established that e^α₁, … ,e^αₙ are algebraically independent whenever α₁, … ,αₙ are algebraic numbers linearly independent over the rationals, is a striking discovery in transcendence theory towards the end of the 19th century. As its extensive generalization, the Schanuel conjecture, according to which the field Q(α₁, … ,αₙ ; e^α₁, … ,e^αₙ) must be of transcendence degree ≥n whenever α₁, … ,αₙ are Q-linearly independent complex numbers, has become a core problem of transcendental number theory. The Ax-Schanuel conjecture, which was resolved in the affirmative by Ax in 1971, was the analogue of the Schanuel conjecture on function fields dealing with the exponential function. The Ax-Schanuel conjecture on Shimura varieties is the analogue in which the exponential map exp: Cⁿ → (C*)ⁿ defined by exp(z₁, … ,zₙ):=(e^z₁, … ,e^zₙ) is replaced by the canonical projection map π_Γ: Ω→Ω/Γ=:X_Γ from a bounded symmetric domain Ω to a quotient Shimura variety X_Γ corresponding to an arithmetic lattice Γ⊂Aut(Ω). The theory of o-minimal structures in mathematical logic especially the counting theorem of Pila-Wilkie (2006), coupled with complex differential geometry and monodromy results on Shimura varieties of Deligne, have led to results on functional transcendence theory notably the Ax-Lindemann theorem of Klingler-Ullmo-Yafaev (2016) and the Ax-Schanuel theorem for the $j$-function of Pila-Tsimerman (2016). Coming from a completely different angle Mok (2019) introduced methods of complex geometry notably those on moduli schemes and their compactifications into functional transcendence theory for not necessarily arithmetic lattices. The latter perspective, coupled with the aforementioned methods and results, together with the theory of tame complex geometry of Peterzil-Strachenko, has led to the proof of the Ax-Schanuel theorem for Shimura varieties by Mok-Pila-Tsimerman (2019). We will also discuss some far-reaching applications of the theorem and its generalizations to number theory notably the uniform Mordell-Lang theorem of Dimitrov-Gao-Habegger (2021) on rational points.

Venue: Physics Lecture Room 4 (A3-2 1F)

7月18日（星期二）下午 15:15-16:15

王贻芳 Yifang Wang

中国科学院院士、

俄罗斯科学院外籍院士、

发展中国家科学院院士、

2015年基础物理学突破奖得主、

中国科学院高能物理研究所所长、

中国科学院大学核科学与技术学院院长

Title

Particle Physics and Its Future --- and Opportunities for China

Abstract

Particle physics is now at the turning point. On the one hand, Standard Model seems so successful with no obvious way towards the future. On the other hand, experimental evidence and theoretical analysis shows that physics beyond the Standard Model do exist. This talk will analyse possible futures of particle physics and suggest a roadmap for China.

Venue: Physics Lecture Room 4 (A3-2 1F)

7月20日（星期四）上午 10:30-11:30

向涛 Tao Xiang

中国科学院院士、

发展中国家科学院院士、

中国科学院物理研究所研究员

Title

Density-matrix and tensor-network renormalization

Abstract

The concept and methodology of the renormalization group is a cornerstone in physics, with far-reaching implications for the study of quantum field theory and critical phenomena. Its impact on the field cannot be overstated. One important direction in the research of many-body quantum theory is the renormalization group study of the so-called tensor-network states. The ultimate goal is to provide a powerful tool for solving correlated quantum problems, such as the mechanism behind high-temperature superconductivity. In this talk, I will delve into the physical background and fundamental ideas that underlie the development of this field. Additionally, I will discuss the latest progress and explore directions for future research. Through this exploration, we hope to gain a deeper understanding of the renormalization group and its potential for further advancing our understanding of the complex phenomena that arise in quantum many-body systems.

Venue: Math Lecture Room 7 (A3-4 1F)

7月24日（星期一）上午 10:30-11:30

陈志明 Zhiming Chen

中国科学院院士、

中国科学院数学与系统科学研究院研究员

Title

Arbitrarily high-order finite element methods for arbitrarily shaped domains with automatic mesh generation

Abstract

Partial different equations with discontinuous coefficients having complex interface geometry are of great interests in practical applications. The design of body-fitted high-order finite element methods requires the construction of shape regular body-fitted meshes for complex geometry and also nonlinear element transforms from the reference element to the elements with curved boundary. In practical applications, it may be challenging to satisfy the conditions imposed on the nonlinear element transforms in the literature which depend on the geometry of the interface. In this talk we study high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems, which release the work of body-fitted mesh generation and provide a natural way to design high-order methods without resorting to nonlinear element transforms. We introduce new concepts of large element and interface deviation to solve the small cut cell problem of unfitted finite element methods. We construct a reliable algorithm to merge small interface elements with their surrounding elements to automatically generate the finite element mesh whose elements are large with respect to both domains. We show novel hp-domain inverse estimates which allow us to prove the stability of the finite element method under practical interface resolving mesh conditions and prove hp a priori and a posteriori error estimates. We propose new basis functions for the interface elements to control the growth of the condition number of the stiffness matrix in terms of the finite element approximation order, the number of elements of the mesh, and the interface deviation. Numerical examples are presented to illustrate the competitive performance of the method. This talk is based on joint works with Ke Li, Yong Liu and Xueshuang Xiang.

Venue: Physics Lecture Room 4 (A3-2 1F)

7月24日（星期一）上午 10:30-11:30

吴岳良 Yue-Liang Wu

中国科学院院士、

发展中国家科学院院士、

国际欧亚科学院院士、

中国科学院大学学术副校长

Title

The Nature of Spacetime and Gravity in Hyperunified Field Theory

Abstract

In this talk, I will show how the general relativity and quantum mechanics can be combined consistently to establish the gravitational quantum field theory (GQFT), which motivates us to build the hyperunified field theory (HUFT) based on the maximum entangled-qubits motion principle as well as gauge and scaling invariance principle. Such a HUFT enables us to understand the nature of spacetime and gravity, and make issues on the basic questions: what is the fundamental building block of nature? what brings about the fundamental symmetry of nature? what is the fundamental interaction of nature? how does the fundamental symmetry govern basic forces? what is the basic structure of spacetime? how many dimensions does spacetime have? why is there only a single temporal dimension? why do we live in a universe with only four-dimensional spacetime? why are there leptons and quarks beyond one family? how does early universe get inflationary expansion? what is a dark matter candidate? what is the nature of dark energy? It is expected that the gravitational wave detections will provide a new window in probing the gravitational universe and exploring the nature of spacetime and gravity.

Venue: Math Lecture Room 7 (A3-4 1F)

7月25日（星期二）上午 08:00-09:00

张平 Ping Zhang

中国科学院院士、

中国科学院数学与系统科学研究院副院长

Title

On the global stability of large Fourier mode for 3-D Navier-Stokes equation

Abstract

In this paper, we first prove the global existence of strong solutions to the 3-D incompressible Navier-Stokes equations with solenoidal initial data, which writes in the cylindrical coordinates is of the form: A(r,z)cosNθ + B(r,z)sinNθ, provided that N is large enough.

In particular, we prove that the corresponding solution has almost the same frequency N for any positive time. The main idea of the proof is first to write the solution in trigonometrical series in θ variable and estimate the coefficients separately in some scale-invariant spaces, then we handle a sort of weighted sum of these norms of the coefficients in order to close the a priori estimate of the solution. Furthermore, we shall extend the above well-posedness result for initial data which is a linear combination of axisymmetric data without swirl and infinitely many large mode trigonometric series in the angular variable. (This is a joint work with Yanlin Liu)

Venue: Math Lecture Room 7 (A3-4 1F)

7月27日（星期四）上午 08:00-09:00

席南华 Nanhua Xi

中国科学院院士、

中国科学院数学与系统科学研究院院长

Title

Infinite dimensional representations of algebraic groups with Frobenius maps

Abstract

We will show that algebraic groups with Frobenius maps have many interesting infinite dimensional irreducible representations, such as an infinite dimensional Steinberg representation is irreducible.

Venue: TCIS Lecture Room 12 (A7 3F)

7月27日（星期四）上午 09:15-10:15

郭雷 Lei Guo

中国科学院院士、

美国电子与电气工程师协会会士（IEEE Fellow）、

发展中国家科学院院士、

瑞典皇家工程科学院外籍院士、

中国科学院国家数学与交叉科学中心主任

Title

Some Basic Problems in Systems and Control

Abstract

In this lecture, a survey of some theoretical progresses on several basic problems in systems and control science will be presented. We will begin by discussing the following two problems that are related to the emergence of complex systems: When flocks with large population will be synchronized? Can a general theory for distributed adaptive filtering be established? Then we will focus on the understanding of the feedback mechanism for regulating uncertain dynamical systems and to answer the following questions: What are the main features of adaptive control systems where online estimators are combined with real-time controllers in the same feedback loop? Can we establish the global stability and optimality of the well-known self-tuning regulators? What is the rationale behind the widespread use of the classical proportional-integral-derivative (PID) control? How about the maximum capability and fundamental limitations of the feedback mechanism in dealing with nonlinear uncertain systems? Finally, we will discuss how a theory may be established for game-based control systems, where some “intelligent” behaviors including dynamical games may exist in the systems to be regulated.