We describe recent work of Klyachko, Totaro, Knutson, and Tao that characterizes
eigenvalues of sums of Hermitian matrices and decomposition of tensor products of …

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 …

We investigate cluster-tilting objects (and subcategories) in triangulated 2-Calabi–Yau and
related categories. In particular, we construct a new class of such categories related to …

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 …

In 1912 Hermann Weyl [W] posed the following problem: given the eigenvalues of two n× n
Hermitian matrices A and B, how does one determine all the possible sets of eigenvalues of …

" There are many bits and pieces of folklore in mathematics that are passed down from
advisor to student, or from collaborator to collaborator, but which are too fuzzy and non …

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 …