Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for
extracting information from data sets, and a beautiful subject in its own right. This book has …

We discuss the geometry of orbit closures and the asymptotic behavior of Kronecker
coefficients in the context of the geometric complexity theory program to prove a variant of …

In this paper we introduce and develop the theory of FI-modules. We apply this theory to
obtain new theorems about:• the cohomology of the configuration space of n distinct ordered …

Determinantal rings and varieties have been a central topic of commutative algebra and
algebraic geometry for several decades. Numerous researchers have contributed to the …

The nearest point map of a real algebraic variety with respect to Euclidean distance is an
algebraic function. For instance, for varieties of low-rank matrices, the Eckart–Young …

Motivated by questions arising in signal processing, computational complexity, and other
areas, we study the ranks and border ranks of symmetric tensors using geometric methods …

In the remarkable paper Graded Betti numbers of Cohen-Macaulay modules and the
multiplicity conjecture, Mats Boij and Jonas Söderberg conjectured that the Betti table of a …

New classes of modules of equations for secant varieties of Veronese varieties are defined
using representation theory and geometry. Some old modules of equations (catalecticant …

Consider the polynomial ring in countably infinitely many variables over a field of
characteristic zero, together with its natural action of the infinite general linear group $ G …

The general Markov model of the evolution of biological sequences along a tree leads to a
parameterization of an algebraic variety. Understanding this variety and the polynomials …