报告题目：Mathematical Developments from the Study of the Integration of the Square Root of a Cubic Polynomial 数学源流：从三次多项式根式积分谈起

报告人：Yum-Tong Siu (Harvard University)

时间：2023年7月6日  16:00-17:00

地点：东区师生活动中心5楼报告厅

报告摘要：

When the degree of the polynomial $P(x)$ is 2, the integral $\int\frac{dx}{\sqrt{P(x)}}$ easily integrates out to an expression involving the inverse sine function. When the degree of $P(x)$ is 3, for example from the simple pendulum problem or from the computation of the arc-length of an ellipse, the situation is completely different. The study of such an integral (known as an elliptic integral) led to the important mathematical developments of the theory of Riemann surfaces, algebraic and K\{a}hler manifolds, moduli problems, Hodge structures and their variations, transcendence problems for numbers and functions, etc. The talk offers a panoramic view. The background material assumed is kept to a minimum to aim for accessibility to a general school-level audience. 

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