From the winner of the Turing Award and the Abel Prize, an introduction to computational
complexity theory, its connections and interactions with mathematics, and its central role in …

This book is an introduction to the representation theory of quivers and finite dimensional
algebras. It gives a thorough and modern treatment of the algebraic approach based on …

Let G be a connected reductive subgroup of a complex connected reductive group ̂G. Fix
maximal tori and Borel subgroups of G and ̂G. Consider the cone LR(G,̂G) generated by …

We study two classes of torsion classes that generalize functorially finite torsion classes, that
is, semistable torsion classes and morphism torsion classes. Semistable torsion classes are …

We use the stabilization functors to study the combinatorial aspects of the-polynomial of a
representation of any finite-dimensional basic algebra. We characterize the vertices of their …

We give an exposition of recent developments in the study of Newell-Littlewood numbers.
These are the tensor product multiplicities of Weyl modules in the stable range. They are …

We introduce the tropical FF‐polynomial f M f_M of a quiver representation M M. We study its
interplay with the general presentation for any finite‐dimensional basic algebra. We give an …

This paper introduces a class of smooth projective varieties that generalize and share many
properties with partial flag varieties of type A. The quiver flag variety M ϑ (Q, r ̲) of a finite …

It is well known that the ring of polynomial invariants of a reductive group is finitely
generated. However, it is difficult to give strong upper bounds on the degrees of the …

Quiver representations arise naturally in many areas across mathematics. Here we describe
an algorithm for calculating the vector space of sections, or compatible assignments of …