报告题目：The magical number four

报 告 人：Harald Upmeier (University of Marburg, Germany)

报告时间：2023.10.24，14:30-15:30

报告地点：金融数学实验室

报告摘要：In this talk, which is addressed to a general audience of students, we explain how the number 4 shows up in very deep relations concerning algebraic operations (solving polynomial equations) and geometric properties related to modern physics. Starting from the real numbers, we construct the complex numbers in detail and explain their basic algebraic and geometric properties. As the main topic of the talk we then introduce the 4-dimensional quaternions (Hamilton numbers) invented by the Irish mathematician Hamilton. We explain how these quaternions play a fundamental role in modern mathematical physics such as the structure of space-time. Finally, we show that there are exactly four steps to construct such algebraic objects and indicate how the fourth step (8 dimensional) will be of fundamental importance in the physics of the future.

报告人简介：

Harald Upmeier，德国Marburge University数学与信息学院教授。Upmeier教授主要研究有界对称域上的Toeplitz算子理论，解析Hilbert模理论以及指标理论等，并做出了许多具有重要国际影响力的研究成果。这些研究工作横跨解析函数空间理论，代数几何，微分几何，李群的表示理论和数学物理等众多领域。其部分研究成果发表在Ann. of Math.，Adv. Math.，J. Reine Angew. Math.，Math. Ann.，Trans. Amer. Math.Soc.，J. Funct. Analysis，Int. Math. Res. Notices等国际一流数学刊物上。

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