Metric algebraic geometry combines concepts from algebraic geometry and differential
geometry. Building on classical foundations, it offers practical tools for the 21st century …

The Hurwitz form of a variety is the discriminant that characterizes linear spaces of
complementary dimension which intersect the variety in fewer than degree many points. We …

We prove that the monodromy group of a reduced irreducible square system of general
polynomial equations equals the symmetric group. This is a natural first step towards the …

This paper is based on the first author's lectures at the 2012 University of Regina Workshop
“Connections Between Algebra and Geometry.” Its aim is to provide an introduction to the …

An enumerative problem on a variety V is usually solved by reduction to intersection theory
in the cohomology of a compactification of V. However, if the problem is invariant under a …

We introduce and study the discriminant of a system of polynomial equations with
indeterminate coefficients, generalizing a number of known special cases, such as the …

We define and study the cyclic Bergman fan of a matroid M, which is a simplicial polyhedral
fan supported on the tropical linear space T (M) of M and is amenable to computational …

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The hyperdeterminant of a polynomial (interpreted as a symmetric tensor) factors into
several irreducible factors with multiplicities. Using geometric techniques these factors are …

In this paper we construct evaluation codes on zero-dimensional complete intersections in
toric varieties and give lower bounds for their minimum distance. This generalizes the results …