Notes on stable currents

Notes on Stable Border Bases

Given X, a set of points whose coordinates are perturbed by errors, we want to determine a “numerically stable” basis B of the vanishing ideal I(X), i.e. for any permitted perturbation X̃ of the original set of points X, only slight changes to the coefficients in B are needed to produce a basis B̃ for the perturbed vanishing ideal I(X̃). We use border bases because they exhibit good numerical stab...

Notes on Stable Maps and Quantum Cohomology

0.1. Overview. The aim of these notes is to describe an exciting chapter in the recent development of quantum cohomology. Guided by ideas from physics (see [W]), a remarkable structure on the solutions of certain rational enumerative geometry problems has been found: the solutions are coefficients in the multiplication table of a quantum cohomology ring. Associativity of the ring yields non-tri...

Notes on: Currents for curve and surface matching

There is a need for registration algorithms to compare functional data, to compute distances between healthy and disease anatomies, and to build probabilistic atlases between the healthy and disease groups. To do this, medical images can be directly processed via 2d or 3d image matching, or after segmentation: extraction of some features points, curves or surfaces of interest. In this case, the...

Notes on the Moduli Space of Stable Quotients

SEMINAR NOTES on Hrushovski’s Stable group theory and approximate subgroups

Next we had talks on Hrushovski’s paper above. The notes below on sections 2 and 3 are a record of talks by Henson and myself, assume only rudimentary knowledge of model theory, and give detailed proofs. If possible we choose notations and formulations similar to those in Hrushovski’s paper. More to follow. Needless to say, the source for all this is [3] to which we also refer for references to...