Geometry Group

Geometry is undergoing significant progress, and its impact is being felt across all areas of mathematics. Researchers are employing techniques from geometry to solve old problems (such as Perelman's resolution of the Poincaré conjecture) and explore new directions. In particular, the study of natural equations that arise in geometry has been a crucial theme, with advanced techniques from the theory of PDEs being employed. The Atiyah-Singer index theorem, developed in the 1960s, established a connection between the theory of linear PDEs, topology, and geometry. While the development of tools for nonlinear PDEs in geometry has been slower, it has resulted in some of the most extraordinary discoveries in mathematics, including Donaldson's breakthroughs in the theory of four-manifolds using the Yang-Mills equations from high-energy physics.”

 
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