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I will start by reviewing an old joint work with Davesh Maulik and Yukinobu Toda on relating Gromov-Witten, Gopakumar-Vafa and stable pair invariants on compact Calabi-Yau 4-folds. For non-compact CY4...
We prove that the quivers with potentials associated by the author to ideal triangulations of punctured surfaces with empty boundary are non-degenerate, provided the number of punctures is 1 or greate...
Let ${mathbb F}_q$ be the finite field of $q$ elements and $k$ be its algebraic closure. Let $Q$ be a quiver with automorphism $sigma$. In this survey we focus on the study of modules over the ${mathb...
Abstract: Let kQ be the path algebra of a quiver Q with its standard grading. We show that the category of graded kQ-modules modulo those that are the sum of their finite dimensional submodules, QGr(k...
Abstract: In a previous paper we have presented a partition formula for the even-index Fibonacci numbers using the preprojective representations of the 3-Kronecker quiver and its universal cover, the ...
Starting from a collection of line bundles on a smooth projective toric DM stack,we give a stacky analogue of the classical linear series construction. We apply our construction to recover the finite ...
We construct noncommutative Donaldson{Thomas invariants associated with abelian orbifold singularities by analysing the instanton contributions to a six-dimensional topological gauge theory.
The category of representations of a Dynkin quiver over local ring R = k[t]/(tn) is not hereditary any more. The Hall algebra defined on this category doesn’t have a well defined coalgebraic structure...
We investigate the connection between representations of posets and those of the corresponding (bound) quivers. As far as quivers are concerned, we concentrate on unitarizable representations which ar...
We associate a coloured quiver to a rigid object in a Hom-finite 2-Calabi–Yau triangulated category and to a partial triangulation on a marked (unpunctured) Riemann surface.
We explore the large-N limits of 2d CFTs, focusing mostly on the WZW model and cosets. The $SU(N)_k$ theory is parametrized in this limit by a 't Hooft-like coupling. We show a duality between strong ...
Let G denote either a special orthogonal group or a symplectic group defined over the complex numbers. We prove the following saturation result for G: given dominant weights λ1, . . . , λr such that...
In the first part of this paper, we prove the existence of torsion free covers in the category of representations of quivers, (Q,R-Mod),for a wide class of quivers included in the class of the so-cal...
Let k be a field and  the n-Kronecker algebra, this is the path algebra of the quiver with 2 vertices, a source and a sink, and n arrows from the source to the sink. It is wellknown that the dimensi...
For an acyclic quiver Q, we solve the Clebsch-Gordan problem for the projective representations by computing the mul-tiplicity of a given indecomposable projective in the tensor product of two indecom...

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