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 …

We develop a comprehensive theory of the stable representation categories of several
sequences of groups, including the classical and symmetric groups, and their relation to the …

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 …

This article is an expository account of the theory of twisted commutative algebras, which
simply put, can be thought of as a theory for handling commutative algebras with large …

In this paper we list a number of open problems and conjectures on Hilbert functions and
syzygies. Some of the problems are closely related to Algebraic Geometry, Combinatorics …

We use results of Eisenbud and Schreyer to prove that any Betti diagram of a graded
module over a standard graded polynomial ring is a positive linear combination of Betti …

Boij–Söderberg theory describes the Betti diagrams of graded modules over the polynomial
ring, up to multiplication by a rational number. Analog Eisenbud–Schreyer theory describes …

This paper studies representation stability in the sense of Church and Farb for
representations of the symmetric group on the cohomology of the configuration space of …

In this article we start with a survey of the recent breakthroughs concerning Betti table of
graded modules over the polynomial ring and cohomology tables coherent sheaves on …

This paper is motivated by the question of understanding the asymptotic behavior of the Betti
numbers of the resolution of the ideal of a projective variety as the positivity of the …