We discuss interactions between quantum mechanics and symplectic
topology including a link between symplectic displacement energy, a
fundamental notion of symplectic dynamics, and the quantum speed
limit, a universal constraint on the speed of...
In the 80s Pitts-Rubinstein conjectured that certain kinds of
Heegaard surfaces in three-manifolds can be isotoped to index 1
minimal surfaces. I'll describe in detail a proof of their
conjecture and some applications. This is joint work with...
We consider the classical problem of prescribing the scalar
curvature of a manifold via conformal deformation of the metric,
dating back to works by Kazdan and Warner. This problem is mainly
understood in low dimensions, where blow-ups of solutions...
