Old and new challenges in Hadamard spaces

Understand

Hadamard spaces have traditionally played important roles in geometry and geometric group theory.

• More recently, they have additionally turned out to be a suitable framework for convex analysis, optimization and nonlinear probability theory.
• The attractiveness of these emerging subject fields stems, inter alia, from the fact that some of the new results have already found their applications both in mathematics and outside.
• Most remarkably, a gradient flow theorem in Hadamard spaces was used to attack a conjecture of Donaldson in Kahler geometry.