Title of the course: Functional Analysis and applications to inverse problem theory
Instructor: Dr. Guillaume Garnier
Institution: Sorbonne Université
Dates: 28 July – 10 August 2025
Prerequisites: Some notion in linear algebra and real analysis
Level: Graduate, advanced undergraduate
Abstract: This course provides a comprehensive introduction to the mathematical framework and techniques of functional analysis and their application to the theory of inverse problems. Functional analysis, as the study of infinite-dimensional vector spaces and linear operators, offers a rigorous foundation for analyzing diverse phenomena in physics, engineering, and applied mathematics. This course covers essential topics, including normed spaces, Banach and Hilbert spaces, bounded and compact operators, and spectral theory. These concepts are then connected to the theory of inverse problems, which seeks to determine unknown causes from observed effects, a ubiquitous challenge in imaging, signal processing, and parameter estimation.
Language: English