Related papers: Tilting and Refined Donaldson-Thomas Invariants

A polarized variety is K-stable if, for any test configuration, the Donaldson-Futaki invariant is positive. In this paper, inspired by classical geometric invariant theory, we describe the space of test configurations as a limit of a direct…

A factorization formula for certain automorphisms of a Poisson algebra associated to a quiver is proved, which involves framed versions of moduli spaces of quiver representations. This factorization formula is related to wall-crossing…

We discuss the construction of $\kappa$-Poincar\'e invariant actions for gauge theories on $\kappa$-Minkowski spaces. We consider various classes of untwisted and (bi)twisted differential calculi. Starting from a natural class of…

We show that motivic Donaldson-Thomas invariants of a~symmetric quiver $Q$, captured by the generating function $P_Q$, can be encoded in another quiver $Q^{(\infty)}$ of (almost always) infinite size, whose only arrows are loops, and whose…

We study the Ginzburg dg algebra $\Gamma_\mathbf{T}$ associated to the quiver with potential arising from a triangulation $\mathbf{T}$ of a decorated marked surface $\mathbf{S}_\bigtriangleup$, in the sense of Qiu. We show that there is a…

Clean isotropic quantum Hall fluids in the continuum possess a host of symmetry-protected quantized invariants, such as the Hall conductivity, shift and Hall viscosity. Here we develop a theory of symmetry-protected quantized invariants for…

We consider a finite dimensional strongly $G$-graded algebra $A$ with { self-injective} $1$-component $B$, and in our main result we prove that the induction from $B$ to $A$ of a basic support $\tau$-tilting pair of $B$-modules is a support…

In our previous papers we introduced categorical invariants, which are, roughly speaking, sets of triangulated subcategories in a given triangulated category and their quotients. Here is extended the list of examples, where these sets are…

In this work we verify consistency of refined topological string theory from several perspectives. First, we advance the method of computing refined open amplitudes by means of geometric transitions. Based on such computations we show that…

Let q be a finite-dimensional Lie algebra and $\theta$ an automorphism of q of order m. We extend $\theta$ to an automorphism of the loop algebra of q and consider the fixed-point subalgebra $q[t,t^{-1}]^{\theta}$. Using a splitting of…

Given a brane tiling on a torus, we provide a new way to prove and generalise the recent results of Szendroi, Mozgovoy and Reineke regarding the Donaldson-Thomas theory of the moduli space of framed cyclic representations of the associated…

We introduce (quantum) twist automorphisms for upper cluster algebras and cluster Poisson algebras with coefficients. Our constructions generalize the twist automorphisms for quantum unipotent cells. We study their existence and their…

In this paper we give a different proof of Quillen's D\'evissage theorem using Barwick's theorem of the heart. The key ingredient is a certain short exact sequence of dg categories, which is closely related with the Auslander-type…

Let k be a perfect field and A a finite dimensional k-algebra of finite global dimension (e.g. the path algebra of a finite quiver without oriented cycles). Making use of the recent theory of noncommutative motives, we prove that the value…

We prove structure theorems for the Donaldson invariants of 4-manifolds with b_+=1, similar to those of Kronheimer and Mrowka in the case b_+>1: We show that for a 4-manifold with b_+=1 and two different period points F, G on the boundary…

We discuss twisted covariance over the noncommutative spacetime algebra generated by the relations [q_theta^mu,q_theta^nu]=i theta^{mu nu}, where the matrix theta is treated as fixed (not a tensor), and we refrain from using the asymptotic…

We study the Donaldson invariants of simply connected $4$-manifolds with $b_+=1$, and in particular the change of the invariants under wall-crossing. We assume the conjecture of Kotschick and Morgan about the shape of the wall-crossing…

For a commutative ring $R$, we define the notions of deformed Picard algebroids and deformed twisted differential operators on a smooth, separated, locally of finite type $R$-scheme and prove these are in a natural bijection. We then define…

We show that variants of the classical reflection functors from quiver representation theory exist in any abstract stable homotopy theory, making them available for example over arbitrary ground rings, for quasi-coherent modules on schemes,…

In a prior paper the authors obtained a four-dimensional discrete integrable dynamical system by the traveling wave reduction from the lattice super-KdV equation in a case of finitely generated Grassmann algebra. The system is a coupling of…