This is the first of a two-volume set that provides a modern account of the representation
theory of finite dimensional associative algebras over an algebraically closed field. The …

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 $ Q $ be a quiver without oriented cycles. For a dimension vector $\beta $ let
$\operatorname {Rep}(Q,\beta) $ be the set of representations of $ Q $ with dimension …

This paper initiates a systematic development of a theory of non-commutative optimization, a
setting which greatly extends ordinary (Euclidean) convex optimization. It aims to unify and …

Symbolic matrices in non-commuting variables, andthe related structural and algorithmic
questions, have a remarkablenumber of diverse origins and motivations. They …

We propose a new second-order method for geodesically convex optimization on the natural
hyperbolic metric over positive definite matrices. We apply it to solve the operator scaling …

We study the left–right action of SL n× SL n on m-tuples of n× n matrices with entries in an
infinite field K. We show that invariants of degree n 2− n define the null cone. Consequently …

The celebrated Brascamp-Lieb (BL) inequalities [BL76, Lie90], and their reverse form of
Barthe [Bar98], are an important mathematical tool, unifying and generalizing numerous in …

In this paper, we present a deterministic polynomial time algorithm for testing whether a
symbolic matrix in non-commuting variables over QQ is invertible or not. The analogous …