标题： S矩阵马拉松的记录：多复变数的美味片段 显示英文标题

标题： Records from the S-Matrix Marathon: Tasty Bits of Several Complex Variables

摘要： 我们将用4次讲座介绍复变函数的基本知识：多个变量的全纯函数的基本性质，伪凸性的概念，CR函数和CR几何，以及$\bar\partial$-问题。 主要的潜在思想是将全纯函数定义域的各种特征联系起来。 在这个过程中，我们将把域上的函数理论与边界几何性质联系起来，并讨论边界值与函数本身之间的关系以及从子空间扩展全纯函数的问题。 这些笔记基于在2024年3月11日至22日于高等研究院举行的S-Matrix马拉松研讨会期间举行的一系列讲座。 显示英文摘要

摘要： We will cover the basics of several complex variables in 4 lectures: Basic properties of holomorphic functions in several variables, the notion of pseudoconvexity, CR functions and CR geometry, and the $\bar\partial$-problem. The main underlying idea is to connect various characterizations of domains of holomorphy, that is, the natural domains of definition for holomorphic functions. In the process we will connect the function theory on the domain to geometric properties of the boundary, and discuss the relationship between the boundary values and the functions themselves and extension of holomorphic functions from subspaces. These notes are based on a series of lectures held during the S-Matrix Marathon workshop at the Institute for Advanced Study on 11-22 March 2024.