中科院数学与系统科学研究院
数学研究所
学术报告
多复变与复几何研讨班
报告人：Prof. Finnur Larusson (University of Adelaide)
题 目：Flexibility in complex geometry
时 间：2023.10.25（星期三）10:00-11:30
地 点：zoom : 853 1274 2956 密码：123456
https://zoom.us/j/85312742956?pwd=a3vhL3W0qi5oiGZCPT7F0aBbAiJVgZ.1
摘 要：Complex geometry lies between smooth geometry and algebraic geometry and exhibits a mix of the flexibility of the former and the rigidity of the latter. The dichotomy of flexibility versus rigidity is a major theme in modern complex geometry. Flexibility means that the obstructions to solving certain important analytic problems are purely topological. It sits within the general context of Gromov's homotopy principle for partial differential relations. Over the past 15 years or so, the study of the h-principle in complex geometry has emerged as a subfield in its own right, known as Oka theory. In the first half of the talk, I will introduce the idea of flexibility and explain the basic notions of Oka theory. Oka theory has turned out to have fruitful connections with many other fields of mathematics, such as minimal surfaces, complex contact geometry, homotopy theory, geometric invariant theory, and dynamical systems. In the second half of the talk, I will present examples of this work, including some very recent results.
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