On super-rigid and uniformly super-rigid operators

Super-rigid Donaldson-Thomas Invariants

We solve the part of the Donaldson-Thomas theory of Calabi-Yau threefolds which comes from super-rigid rational curves. As an application, we prove a version of the conjectural Gromov-Witten/DonaldsonThomas correspondence of [MNOP] for contributions from super-rigid rational curves. In particular, we prove the full GW/DT correspondence for the quintic threefold in degrees one and two.

Rigid surface operators

Surface operators in gauge theory are analogous to Wilson and ’t Hooft line operators except that they are supported on a two-dimensional surface rather than a one-dimensional curve. In a previous paper, we constructed a certain class of half-BPS surface operators in N = 4 super Yang–Mills theory, and determined how they transform under S-duality. Those surface operators depend on a relatively ...

On elliptic operators and non-rigid shapes

Many shape analysis methods treat the geometry of an object as a metric space captured by the Laplace-Beltrami operator. In this thesis we present an adaptation of a classical operator from quantum mechanics to shape analysis where we suggest to integrate a scalar function through a unified elliptical Hamiltonian operator. We study the addition of a potential function to the Laplacian as a gene...

Subordination and Super Ordination Results Involving Certain Convolution Operators

subordination and super ordination results involving certain convolution operators