Stability for functional and geometric inequalities
Tensor rank
Prescribing scalar curvature in high dimension
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 are proven to be "isolated simple". We find natural conditions to guarantee this also in arbitrary dimensions, when the prescribed curvatures are Morse functions. As a consequence, we improve some pinching conditions in the literature and derive existence
results of new type. This is joint work with M. Mayer.
Cosmological Correlators from the Boundary
Cosmological Correlators from the Boundary
On the existence of minimal Heegaard splittings
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 Liokumovich and Song.