Geometric Spectral Theory and Applications

Date: 7 January - 26 June 2026

Location: Isaac Newton Institute

The primary objective of this programme is to address the latest developments in geometric spectral theory.  In recent years, the field has seen significant breakthroughs, leading to progress toward the resolution of some long-standing conjectures. These advancements have been achieved with the help of novel techniques, with applications extending beyond the scope of the subject. At the same time, there remain many intriguing open problems and challenges.  The focus of the programme will be on four interconnected themes: 

• Eigenvalues and geometry
• Geometry of eigenfunctions and spectral asymptotics
•  Probabilistic and number-theoretic methods in geometric spectral theory
• Numerical aspects and applications 

 The program will feature a series of engaging activities aimed to foster collaboration between participants and stimulate new ideas. There will be four week-long workshops on each theme, complemented by informal intensive working weeks focused on tackling some of the main open questions in the field. The fifth workshop will specifically target early career reserachers in the field. The regularly held seminars and survey talks will provide a platform for sharing insights and advancements. 

CMI Enhancement and Partnership Program