Andrea Malchiodi, Ph.D.
Professor of Mathematics
Scuola Normale Superiore
Florence, Italy
The Yamabe problem is an extension to manifolds of dimension greater or equal to three of the classical Uniformization question for Riemann surfaces. Formulated in 1960, it serves as a paradigm for geometric partial differential equations exhibiting a lack of compactness. Although the existence of solutions was fully settled in the 1980s through the landmark contributions of Trudinger, Aubin and Schoen, the problem has recently revealed new and surprising aspects. In this talk, we will discuss the foundational results in the literature, alongside current perspectives and open problems.