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。
多位院士领衔主讲大会报告
美国科学院院士、美国国家工程院院士、美国艺术与科学院院士
美国加利福尼亚大学伯克利分校教授
Michael Jordan
美国国家工程院院士
英国皇家科学院院士
欧洲科学院院士、英国牛津大学教授
Nick Trefethen
新加坡科学院院士
发展中国家科学院院士
新加坡国立大学教授
沈佐伟
日本学士院院士
美国纽约州立大学石溪分校教授
Kenji Fukaya
美国艺术与科学院院士
美国麻省理工学院教授
Scott Sheffield
2002年菲尔兹奖得主、法国科学院院士
法国高等科学研究所终身教授
Laurent Lafforgue
6场报告
7月17日—7月21日
Venue：TCIS Lecture Room 12 (A7 3F)
7月17日（星期一）下午 13:30-14:30
迈克尔·乔丹
Michael Jordan
美国科学院院士、美国工程院院士、美国艺术与科学院院士、
美国加利福尼亚大学伯克利分校教授
Title
An alternative view on AI: Collaborative learning, incentives, and social welfare
Abstract
Artificial intelligence (Al) has focused on a paradigm in which intelligence inheres in a single, autonomous agent. Social issues are entirely secondary in this paradigm. When Al systems are deployed in social contexts, however, the overall design of such systems is often naive--a centralized entity provides services to passive agents and reaps the rewards. Such a paradigm need not be the dominant paradigm for information technology. In a broader framing, agents are active, they are cooperative, and they wish to obtain value from their participation in learning-based systems. Agents may supply data and other resources to the system, only if it is in their interest to do so. Critically, intelligence inheres as much in the overall system as it does in individual agents, be they humans or computers. This is a perspective familiar in the social sciences and a first goal in this line of work is to bring economics into contact with the computing and data sciences. The long-term goal is two-fold--to provide a broader conceptual foundation for emerging real-world Al systems, and to upend received wisdom in the computational, economic, and inferential disciplines.
Venue：Math Lecture Room 8 (A3-4 3F)
7月17日（星期一）下午 13:30-14:15
尼克·特雷费森 Nick Trefethen
美国国家工程院院士、英国皇家学会院士、欧洲科学院院士、
英国牛津大学教授
Title
The AAA algorithm for rational approximation
Abstract
With this new algorithm, approximation by rational functions has become fast and practical in a way it was not before. We will discuss many examples and applications including the solution of partial differential equations.
Venue：Math Lecture Room 9 (A6 1F)
7月19日（星期三）下午 16:00-17:00
沈佐伟 Zuowei Shen
新加坡国家科学院院士、
发展中国家科学院院士、
新加坡国立大学教授
Title
Deep Approximation via Deep Learning
Abstract
The primary objective of many applications is to approximate or estimate a function using samples obtained from a probability distribution on the input space. Deep approximation involves approximating a function by composing numerous layers of simple functions, which can be seen as a sequence of nested feature extractors. The fundamental concept of deep learning networks is to convert these layers of compositions into layers of adjustable parameters that can be fine-tuned through a learning process, ultimately achieving a high-quality approximation based on the input data. In this presentation, we will delve into the mathematical theory behind this innovative approach and explore the approximation rate of deep networks. Additionally, we will highlight the distinctions between this new approach and traditional approximation theory, and demonstrate how this novel theory can be leveraged to comprehend and design deep learning network.
Venue：Math Lecture Room 9 (A6 1F)
7月20日（星期四）上午 8:00-9:00
深谷贤治 Kenji Fukaya
日本学士院院士、
美国纽约州立大学石溪分校教授
Title
An infinity category and Floer homology
Abstract
Floer homology is a half infinite dimensional homology theory invented by A Floer 40 years ago. The further study of the structure in Floer theory shows a kind of higher category theory is useful. I will survey this topic including its application to Symlectic Geometry and Gauge theory.
ICBS Lecture
Mathematics
Venue：Math Lecture Room 3 (A3-1a 2F)
7月20日（星期四）下午 14:00-14:45
斯科特·谢菲尔德
Scott Sheffield
美国艺术与科学院院士、
美国麻省理工学院教授
Title
How to build a random surface
Abstract
The theory of "random surfaces" has emerged in recent decades as a significant field of mathematics, lying somehow at the interface between geometry, probability, combinatorics, analysis and mathematical physics. Just as Brownian motion is a special kind of random path, there is a similarly special kind of random surface, which is characterized by special symmetries, and which arises in many different contexts. Random surfaces are often motivated by physics: statistical physics, string theory, quantum field theory, and so forth. They have also been independently studied by mathematicians working in random matrix theory and enumerative graph theory. But even without that motivation, one may be drawn to wonder what a "typical" two-dimensional manifold look likes, or how one can make sense of that question. I will give a broad overview of what this theory is about, including many computer simulations and illustrations. ln particular, I will highlight some recent works with Jason Miller in which we proved the equivalence of Liouville quantum gravity and the Brownian sphere -- two random surface models that were historically defined in completely different ways.
Venue：Math Lecture Room 9 (A6 1F)
7月21日（星期五）上午 9:15-10:15
洛朗·拉福格 Laurent Lafforgue
2002年菲尔兹奖得主、
法国科学院院士、
法国高等科学研究所终身教授
Title
Towards a geometric theory of cohomology functors: the case of degree 0
Abstract
We will explain how Olivia Caramello's proposed approach for constructing a Galois-type theory of cohomology functors can be implemented and fully verified in the case of cohomology of degree 0. The models of this theory-or equivalently the points of the associated Classifying Topos-are exactly cohomology functors of degree 0. As its Classifying Topos is Galois, this theory is complete, which means that all its models share the same geometric-logic properties. In particular, their components at all different geometric objects all have the same dimensions and the same algebraic structures. These results are already non-trivial and can be considered as toy-models for cohomology in higher degrees, which is the objective of Caramello's proposed approach.
