From Local to Global Holomorphic Peak Functions - Lecture 1

Explore the intricacies of holomorphic peak functions in this lecture by Gautam Bharali from the International Centre for Theoretical Sciences. Delve into the transition from local to global perspectives, examining key concepts such as utility instances, definitions, and meta-theorems. Analyze the general prescriptions and conditions for holomorphic peak functions, followed by crucial observations and a detailed proof. Learn about the construction of auxiliary functions and their significance in the field. Gain valuable insights into complex analysis and its applications in higher dimensions, suitable for graduate students, postdocs, and early-career researchers with a strong foundation in complex analysis and calculus of several variables.

From local to global homomorphic peak
Utility: instances
Definition
Meta - Theorem
Conditions: Every known General prescription
Observations
Proof
Step 2: Constructing an auxiliary function
Result: We'll need