Since its inception around 1980, the theory of perverse sheaves has been a vital tool of
fundamental importance in geometric representation theory. This book, which aims to make …

This is the first in a series of papers presenting a new understanding of scattering
amplitudes based on fundamentally combinatorial ideas in the kinematic space of the …

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 …

For a finite-dimensional algebra A over a field K with n simple modules, the real
Grothendieck group K 0 (proj A) R:= K 0 (proj A)⊗ ZR≅ R n gives stability conditions of King …

We study the log-likelihood function and maximum likelihood estimate (MLE) for the matrix
normal model for both real and complex models. We describe the exact number of samples …

A nilpotent endomorphism of a quiver representation induces a linear transformation on the
vector space at each vertex. Generically among all nilpotent endomorphisms, there is a well …

We study the Rouquier dimension of wrapped Fukaya categories of Liouville manifolds and
pairs, and apply this invariant to various problems in algebraic and symplectic geometry. On …

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 give a moduli-theoretic treatment of the existence and properties of moduli spaces of
semistable quiver representations, avoiding methods from geometric invariant theory. Using …

For any given finite subgroup $ G\subset SL_3 (\mathbb {C}) $, we show that every
projective crepant resolution $ X $ of the quotient variety $\mathbb {C}^ 3/G $ is isomorphic …