We study methods for finding the solution set of a generic system in a family of polynomial
systems with parametric coefficients. We present a framework for describing monodromy …

Why is it that semidefinite relaxations have been so successful in numerous applications in
computer vision and robotics for solving non-convex optimization problems involving …

Babai's conjecture states that, for any finite simple non-abelian group $ G $, the diameter of
$ G $ is bounded by $(\log| G|)^{C} $ for some absolute constant $ C $. We prove that, for …

We prove a version of Jordan's classification theorem for finite subgroups of $\mathrm {GL} _
{n}(K) $ that is at the same time quantitatively explicit, CFSG-free, and valid for arbitrary $ K …

This article discusses the design of the Apprenticeship Program at the Fields Institute, held
21 August–3 September 2016. Six themes from combinatorial algebraic geometry were …

Polynomial systems of equations that occur in applications frequently have a special
structure. Part of that structure can be captured by an associated Galois/monodromy group …

We study the problem of how many different sum of squares decompositions a general
polynomial f with SOS-rank k admits. We show that there is a link between the variety SOS k …

We introduce and study coordinate-wise powers of subvarieties of P^ n P n, ie varieties
arising from raising all points in a given subvariety of P^ n P n to the r-th power, coordinate …

Stewart--Gough platforms are mechanisms which consist of two rigid objects, a base and a
platform, connected by six legs via spherical joints. For fixed leg lengths, a generic Stewart …

Low-rank approximation of kernels is a fundamental mathematical problem with widespread
algorithmic applications. Often the kernel is restricted to an algebraic variety, eg, in problems …