7月25日，上海复旦大学迎来了一位世界级的数学大师——安德烈·奥昆科夫教授。奥昆科夫，作为2006年菲尔兹奖得主，以其在数学领域尤其是表示论、代数几何、动力系统、组合学、概率论、弦理论、统计力学等多个领域的卓越贡献而闻名。在此次“浦江科学大师讲坛”上，奥昆科夫以“表示论的源头与硕果”为主题，向现场听众分享了他在数学领域的独到见解。
奥昆科夫教授以中文作为开场白，用一句“中文是一门很复杂的语言，对我而言充满挑战，就像数学对很多人而言充满挑战一样”亲切地问候了在场的听众。这一简洁而富有深意的开场，不仅展示了他对中文学习的投入，也体现了他对数学作为一门复杂而美丽的学科的深刻理解。
在演讲中，奥昆科夫教授追溯了表示论的起源，强调了其对数学理论的深远影响。他表示，人类对对称性的追求是表示论诞生的驱动力。从古希腊时代的朴素对称观念，到现代数学家通过抽象符号，如“群”的概念，给出了对对称性更系统、更抽象的数学描述，表示论的诞生展现了数学的逻辑美与深刻性。
奥昆科夫教授进一步指出，作为相对年轻的数学领域，表示论在20世纪后半叶迅速发展，并与物理、化学等学科呈现出交叉融合的趋势。他强调表示论在理论物理、计数几何等研究领域的重要性，并指出表示论与其他学科结合的研究是一个重要且充满潜力的方向。他表示，通过将数学理论应用于解决具体问题，可以进一步深化对相关理论的理解，这也为数学与实际应用的桥梁搭建提供了新的可能。
奥昆科夫教授还分享了他与中国数学界的密切合作与交流，包括在2023年11月当选为中国科学院外籍院士，并多次访问中国高校与年轻学者交流。他鼓励研究人员找到自己真正热爱的研究领域，而非强迫自己从事不感兴趣的领域，这一观点体现了他对数学研究者个人成长与兴趣驱动的重视。
此次演讲不仅为在场的听众提供了一场学术盛宴，也展示了奥昆科夫教授对数学之美与应用潜力的深刻洞察，以及他对促进国际学术交流与合作的贡献。通过奥昆科夫教授的分享，听众们不仅对表示论有了更深入的理解，也对数学作为一门跨学科、创新性的科学领域有了更全面的认识。
英语如下：
### Fields Medalist Okounkov Shares Insights on AI Era: Don’t Forget Classical Mathematical Theories
#### July 25, World-Class Mathematician Andrei Okounkov Lectures in Shanghai: Focus on AI Without Forgetting Classic Theories
On July 25, the renowned mathematician Professor Andrei Okounkov, a Fields Medalist from 2006, brought his expertise in mathematics, particularly in representation theory, algebraic geometry, dynamical systems, combinatorics, probability theory, string theory, and statistical mechanics, to the audience at Fudan University in Shanghai. His lecture, titled “The Origins and Achievements of Representation Theory,” was part of the “Pudong Science Masters’ Forum,” where he shared his profound insights into the mathematical field.
Professor Okounkov began his talk in Chinese, addressing the audience with the endearing phrase, “Chinese is a very complex language, a challenge for me just like math is for many,” which not only showcased his dedication to learning Chinese but also reflected his deep understanding of the complexity and beauty of mathematics.
In his presentation, Professor Okounkov traced the origins of representation theory, highlighting its profound impact on mathematical theory. He emphasized that the quest for symmetry drives the birth of representation theory, from the simple notions of symmetry in ancient Greek times to the modern mathematical description of symmetry through abstract concepts like “groups.” This exposition revealed the logical elegance and depth of mathematics.
He further explained that, as a relatively young field, representation theory has rapidly developed in the latter half of the 20th century, intersecting with disciplines such as physics, chemistry, and showing the potential for interdisciplinary research. He underscored the importance of representation theory in theoretical physics, counting geometry, and other research areas, and highlighted the significance of combining representation theory with other fields. He pointed out that applying mathematical theories to solve specific problems can deepen understanding of related theories, offering new possibilities for bridging mathematics with practical applications.
Professor Okounkov also shared his close collaboration and exchanges with Chinese mathematicians, including his election as an honorary member of the Chinese Academy of Sciences in November 2023 and his multiple visits to Chinese universities and young scholars. He encouraged researchers to find their true passion in research, rather than forcing themselves into uninteresting fields, reflecting his emphasis on the importance of personal growth and interest-driven research in mathematics.
This lecture not only provided an academic feast for the audience but also showcased Professor Okounkov’s deep insight into the beauty and potential applications of mathematics, as well as his contribution to international academic exchanges and cooperation. Through his sharing, the audience gained a deeper understanding of representation theory and a more comprehensive recognition of mathematics as a cross-disciplinary and innovative scientific field.
【来源】http://www.chinanews.com/sh/2024/07-25/10257557.shtml
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