地点：海纳苑2幢204室

时间：9月17日，16:15 - 17:35

报告人：Siarhei Finski（巴黎综合理工学院）

摘要:  

Pretalk: Metric entropy and Hilbert's thirteenth problem

Abstract: How much information does it take to pin down a function within a prescribed accuracy? Pontryagin-Schnirelmann and Kolmogorov made this question precise through metric entropy: the least number of balls of a given radius needed to cover a compact subset of a metric space. I will recall the necessary definitions, compute a few elementary examples, and explain the historical motivation through Hilbert's thirteenth problem.

Research talk: Metric entropy of the space of holomorphic functions

Abstract: Fix a compact subset of a complex manifold and consider the continuous functions on it that admit uniformly bounded holomorphic extensions to the whole manifold. Montel's theorem says this family is compact in the uniform topology. I will make that compactness quantitative by determining the asymptotics of its metric entropy, which settles a problem of Kolmogorov for arbitrary domains in arbitrary Stein manifolds. After stating the result, I will explain how the proof connects to recent developments in complex and algebraic geometry, approximation theory, and pluripotential theory.