Noncommutative geometry has emerged as a powerful mathematical framework that extends classical differential geometry by incorporating new structures that naturally encode both analytic and geometric data. Initially developed as a means of describing spaces whose traditional geometric intuition breaks down, noncommutative geometry provides a unifying perspective in which analysis, topology, and algebraic structures interact seamlessly. The key idea is to replace classical spaces with operator algebras, allowing for the study of geometric and topological properties through spectral and functional-analytic methods.

This workshop aims to achieve the following outcomes:

• Provide participants with a deep understanding of the fundamental principles of noncommutative geometry.
• Explore applications of noncommutative geometry in quantitative geometry and topology, number theory, global analysis, and representation theory.
• Foster collaboration among researchers by facilitating discussions on recent advances and open problems in the field.
• Introduce computational and spectral techniques that enable new insights into noncommutative spaces.
• Encourage interdisciplinary dialogue between mathematicians in neighbouring fields and identify new research directions.
• Develop a roadmap for future research and potential applications of noncommutative geometry in any of the four domains which will form the backbone of our activity