The boundedness (on $L^p$ spaces) of commutators $[b,T] = bT-Tb$ of pointwise multiplication $b$ and singular integral operators $T$ has been well studied for a long time. Curiously, the necessary ...

Classical invariant theory has essentially addressed the action of the general linear group on homogeneous polynomials. Yet the orthogonal group arises in applications as the relevant group of ...

Hyperkähler manifolds are higher-dimensional analogs of K3 surfaces. Verbitsky and Markmann recently proved that their period map is an open embedding. In a joint work with E. Macri, we explicitly ...

Quantum optical systems provides one of the best physical settings to engineer quantum many-body systems of atoms and photons, which can be controlled and measured on the level of single quanta. In ...