Given a category $\mathcal {C} $ of a combinatorial nature, we study the following
fundamental question: how do combinatorial properties of $\mathcal {C} $ affect algebraic …

This book presents a systematic treatment of Grobner bases in several contexts. The book
builds up to the theory of Grobner bases for operads due to the second author and …

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 …

We prove that any finite-degree polynomial functor over an infinite field is topologically
Noetherian. This theorem is motivated by the recent resolution, by Ananyan-Hochster, of …

Using the language of twisted skew-commutative algebras, we define secondary
representation stability, a stability pattern in the unstable homology of spaces that are …

This is the first in a series of papers in which we study representations of the Brauer category
and its allies. We define a general notion of triangular category that abstracts key properties …

Let P 3 (k∞) be the space of cubic polynomials in infinitely many variables over the
algebraically closed field k (of characteristic≠ 2, 3). We show that this space is GL∞ …

We study GL-equivariant modules over the infinite variable polynomial ring $ S= k [x_1,
x_2,..., x_n,...] $ with $ k $ an infinite field of characteristic $ p> 0$. We extend many of Sam …

Let VI be the category of finite dimensional F q-vector spaces whose morphisms are injective
linear maps and let k be a noetherian ring. We study the category of functors from VI to k …