“In my opinion, the highlight of the workshop was the merging of two topics which normally are dealt with separately: the world of nonlinear PDE’s and that of spectral geometry. These two topics share deep geometric problems, and looking at those problems from different perspectives was really a success of the meeting.”

“It is certainly of great academic value, with a line up of excellent speakers from closely related subfields of geometric analysis and plenty of room for fruitful exchange of ideas.”

Geometric analysis had intrigued mathematicians for centuries and remains a vibrant area of modern mathematics. Central to this field were the formulation of both linear and nonlinear partial differential equations (PDEs) on manifolds and the minimization of energy functionals in infinite-dimensional spaces. Our workshop would focus on four closely interconnected areas within geometric analysis: characterizing solutions to PDEs, Euler equations, minimal surface theory, and spectral geometry. The event aimed to bring together leading experts and early-career researchers from around the world to discuss the latest advancements, exchange ideas, and explore major challenges and open problems in the field.

We acknowledged the support of the London Mathematical Society and Glasgow Mathematical Journal Trust. The event organised in partnership with the Clay Mathematics Institute.