In the applied sciences one is often confronted with free boundaries, which arise when the solution to a problem consists of a pair: a function u (often satisfying a partial differential equation (PDE...

Donaldson-Thomas (DT) theory is an enumerative theory which counts ideal sheaves of curves on a Calabi-Yau 3-fold. Motivic Donaldson-Thomas theory is a categorification of the DT theory. This...

The number of embedded pseudo-holomorphic curves in a symplectic manifold typically depends on the choice of an almost complex structure on the manifold and so does not lead to a symplectic invariant...

Spherical Designs are sets of points on the sphere with the property that the average of a low-degree polynomial over the points is the same as the average on the sphere. They are classical yet full...